Deck 60: Introduction to Conics Parabolas

Question 1

Find the vertex and focus of the parabola from the given equation and select its graph.​ $$y = \frac { 1 } { 6 } x ^ { 2 }$$ ​

A)Vertex: (0,0) Focus: (0,-1.5) ​
B)Vertex: (0,0) Focus: (-1.5,0)
C)Vertex: (0,0) Focus: (0,1.5)
D)Vertex: (0,0) Focus: (0,1.5)
E)Vertex: (0,0) Focus: (0,-1.5)

Answer 1

Vertex: (0,0) Focus: (0,1.5)

Question 2

Find the vertex and focus of the parabola from the given equation and select its graph.​ $$x ^ { 2 } + 16 y = 0$$ ​

A)Vertex: (0,0) Focus: (4,0)
B)Vertex: (0,0) Focus: (-4,0)
C)Vertex: (0,-4) Focus: (0,0)
D)Vertex: (0,0) Focus: (0,4)
E)Vertex: (0,0) Focus: (0,-4)

Answer 2

Vertex: (0,0) Focus: (0,-4)

Question 3

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.​ $$\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$$ ​

A)Center: (0,0) Vertices: (-6,0)
​
B)Center: (0,0) Vertices: (±6,0)
​
C)Center: (0,0) Vertices: (-6,0)
​
D)Center: (0,0) Vertices: (±6,0)
​
E)Center: (0,0) Vertices: (6,0)
​

Answer 3

Center: (0,0) Vertices: (±6,0)
​

Question 4

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Directrix: y = 2
​

A) $x ^ { 2 } = - 8 y$
B) $x ^ { 2 } = 8 y$
C) $y ^ { 2 } = - 8 x$
D) $y ^ { 2 } = 8 x$
E) $x ^ { 2 } = - \frac { y } { 8 }$

Question 5

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Directrix: x = 3
​

A) $x ^ { 2 } = - 12 y$
B) $y ^ { 2 } = 12 x$
C) $y ^ { 2 } = \frac { x } { 12 }$
D) $x ^ { 2 } = 12 y$
E) $y ^ { 2 } = - 12 x$

Question 6

Find the vertex and focus of the parabola from the given equation and select its graph.​ $$2 x + y ^ { 2 } = 0$$ ​

A)Vertex: (0,0) Focus: (- $\frac { 1 } { 2 }$ ,0)
B)Vertex: (- $\frac { 1 } { 2 }$ ,0) Focus: (0,0)
C)Vertex: (0,0) Focus: (0, $\frac { 1 } { 2 }$ )
D)Vertex: (0,0) Focus: (0,- $\frac { 1 } { 2 }$ )
E)Vertex: (0,0) Focus: ( $\frac { 1 } { 2 }$ ,0)

Question 7

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Passes through the point (2,4);horizontal axis
​

A) $x ^ { 2 } = 8 y$
B) $x ^ { 2 } = - 8 y$
C) $y ^ { 2 } = 8 x$
D) $y ^ { 2 } = - 8 x$
E) $y ^ { 2 } = \frac { x } { 8 }$

Question 8

Find the vertex and focus of the parabola for the given equation and select its graph.​ $$y = - 3 x ^ { 2 }$$ ​

A)Vertex: (0,0) Focus: (0,3)
B)Vertex: (0,0) Focus: (0,-12)
C)Vertex: (0,0) Focus: (0,-3)
D)Vertex: (0,0) Focus: $$\left( 0 , - \frac { 1 } { 12 } \right)$$
E)Vertex: (0,0) Focus: $$\left( 0 , \frac { 1 } { 3 } \right)$$

Question 9

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Focus: (0, $\frac { 1 } { 2 }$ )
​

A) $y ^ { 2 } = - 2 x$
B) $x ^ { 2 } = - 2 y$ ​
C) $y ^ { 2 } = 2 x$
D) $x ^ { 2 } = 2 y$
E) $x ^ { 2 } = \frac { y } { 2 }$

Question 10

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.​ $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 1 / 9 } = 1$ ​

A)Center: (0,0) Vertices: (±3,0)
B)Center: (0,0) Vertices: (-3,0)
C)Center: (0,0) Vertices: (3,0)
​
D)Center: (0,0) Vertices: (±3,0)
​
E)Center: (0,0) Vertices: (-3,0)
​

Question 11

Select the standard form of the equation of the parabola and determine the coordinates of the focus.​ ​

A) $x ^ { 2 } = \frac { 5 } { 2 } y$ ;Focus: $\left( 0 , \frac { 5 } { 8 } \right)$
B) $y ^ { 2 } = - \frac { 5 } { 2 } x$ ;Focus: $\left( - \frac { 5 } { 8 } , 0 \right)$
C) $x ^ { 2 } = - \frac { 5 } { 2 } y$ ;Focus: $$\left( 0 , - \frac { 5 } { 8 } \right)$$
D) $y ^ { 2 } = \frac { 5 } { 2 } x$ ;Focus: $\left( \frac { 5 } { 8 } , 0 \right)$
E) $y ^ { 2 } = \frac { 5 } { 2 } x$ ;Focus: $( 5,0 )$

Question 12

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$ ​

A) $x ^ { 2 } = 14 y$
B) $y ^ { 2 } = - 14 x$
C) $y ^ { 2 } = 14 x$
D) $x ^ { 2 } = - 14 y$
E) $y ^ { 2 } = - \frac { x } { 14 }$

Question 13

Find the vertex and focus of the parabola from the given equation and select its graph.​ $$y ^ { 2 } = 6 x$$ ​

A)Vertex: (0,0) Focus: (- $\frac { 3 } { 2 }$ ,0)
B)Vertex: (0,0) Focus: (0,- $\frac { 3 } { 2 }$ )
C)Vertex: (0,0) Focus: ( $\frac { 3 } { 2 }$ ,0)
D)Vertex: (0,0) Focus: (0, $\frac { 3 } { 2 }$ )
E)Vertex: (0,0) Focus: ( $\frac { 3 } { 2 }$ ,0)

Question 14

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Passes through the point $\left( - 5 , \frac { 1 } { 3 } \right)$ ;vertical axis
​

A) $x ^ { 2 } = 75 y$
B) $x ^ { 2 } = - 75 y$
C) $y ^ { 2 } = - 75 x$
D) $y ^ { 2 } = 75 x$
E) $x ^ { 2 } = \frac { y } { 75 }$

Question 15

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Directrix: x = -4
​

A) $y ^ { 2 } = - 16 x$
B) $y ^ { 2 } = 16 x$
C) $x ^ { 2 } = - 16 y$
D) $x ^ { 2 } = 16 y$
E) $y ^ { 2 } = \frac { x } { 16 }$

Question 16

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Focus: (0,-2)
​

A) $y ^ { 2 } = 8 x$
B) $x ^ { 2 } = - 8 y$
C) $y ^ { 2 } = - 8 x$
D) $x ^ { 2 } = 8 y$
E) $x ^ { 2 } = - \frac { y } { 8 }$

Question 17

Find the vertex and focus of the parabola for the given equation and select its graph.​ $$y ^ { 2 } = - 4 x$$ ​

A)Vertex: (0,0) Focus: (1,0)
B)Vertex: (0,0) Focus: (1,0)
C)Vertex: (0,0) Focus: (-1,0)
D)Vertex: (0,0) Focus: ( - 1,0)
E)Vertex: (0,0) Focus: (0,1)

Question 18

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.​ $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 49 } = 1$ ​

A)Center: (0,0) Vertices: (±10,0)
​
B)Center: (0,0) Vertices: (10,0)
C)Center: (0,0) Vertices: (-10,0)
​
D)Center: (0,0) Vertices: (-10,0)
​
E)Center: (0,0) Vertices: (±10,0)
​

Question 19

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Focus: (-4,0)
​

A) $y ^ { 2 } = - 16 x$
B) $$y ^ { 2 } = 16 x$$
C) $$x ^ { 2 } = - 16 y$$
D) $x ^ { 2 } = - 16 y$
E) $y ^ { 2 } = - \frac { x } { 16 }$

Question 20

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Directrix: y = -1
​

A) $y ^ { 2 } = 4 x$
B) $x ^ { 2 } = - \frac { y } { 4 }$
C) $x ^ { 2 } = 4 y$
D) $y ^ { 2 } = - 4 x$
E) $x ^ { 2 } = - 4 y$

Question 21

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0,-1)

A)y² = -4x
B)x² = -4y
C)x² = y
D)y² = -x
E)x² = -y

Question 22

Identify the conic.​ $4 y ^ { 2 } + 5 x ^ { 2 } - 20 = 0$ ​

A)Ellipse
B)Circle
C)Parabola
D)Line
E)Hyperbola

Question 23

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -5
​

A)y² = 20x
B)y² = -5x
C)x² = -20y
D)x² = -5y
E)x² = 20y

Question 24

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (±3,0);passes through the point ​ $( 5 , \sqrt { 3 } )$ ​

A) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 27 / 16 } = - 1$
B) $\frac { x ^ { 2 } } { 27 / 16 } + \frac { y ^ { 2 } } { 9 } = 1$
C) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 27 / 16 } = 1$
D) $\frac { x ^ { 2 } } { 27 / 16 } + \frac { y ^ { 2 } } { 9 } = - 1$
E) $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 27 / 16 } = 1$

Question 25

Find the center and vertices of the hyperbola and select its graph,using asymptotes as sketching aids.​ $4 y ^ { 2 } - 25 x ^ { 2 } = 100$ ​

A)Centre: (0,0) Vertices: (0,-5)
B)Centre: (0,0) Vertices: (±5,0)
C)Centre: (0,0) Vertices: (0,±5)
D)Centre: (0,0) Vertices: (0,5)
E)Centre: (0,0) Vertices: (5,0)

Question 26

Find the center and vertices of the hyperbola and sketch its graph,using asymptotes as sketching aids.​ $$\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$$ ​

A)Center: (0,0) Vertices: (-5,0)
B)Center: (0,0) Vertices: (-3,0)
C)Center: (0,0) Vertices: (3,0)
D)Center: (0,0) Vertices: (±5,0)
E)Center: (0,0) Vertices: (±3,0)

Question 27

Select the standard form of the equation of the parabola and determine the coordinates of the focus. ​​ ​

A) $y ^ { 2 } = - \frac { 49 } { 5 } x$ ;Focus: $\left( \frac { 49 } { 20 } , 0 \right)$
B) $y ^ { 2 } = \frac { 49 } { 5 } x$ ;Focus: $\left( \frac { 49 } { 20 } , 0 \right)$
C) $y ^ { 2 } = - \frac { 49 } { 5 } x$ ;Focus: $\left( - \frac { 49 } { 20 } , 0 \right)$
D) $x ^ { 2 } = - \frac { 49 } { 5 } y$ Focus: $\left( \frac { 49 } { 20 } , 0 \right)$
E) $x ^ { 2 } = \frac { 49 } { 5 } y$ ;Focus: $\left( \frac { 49 } { 20 } , 0 \right)$

Question 28

Find the vertex and focus of the parabola. $x ^ { 2 } + 8 y = 0$ ​

A)vertex: (0,0)focus: (0,-2)
B)vertex: (2,0)focus: (0,0)
C)vertex: (0,0)focus: (-2,0)
D)vertex: (0,0)focus: (0,2)
E)vertex: (-2,0)focus: (0,0)

Question 29

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (0,±3);focies: (0,±7)
​ ​

A) $- \frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$
B) $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = 1$
C) $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 40 } = 1$
D) $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = - 1$
E) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$

Question 30

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin. L = 5 inches

A) $y = 5 x ^ { 2 }$
B) $x ^ { 2 } = 5 y$
C) $y = 20 x ^ { 2 }$
D) $x ^ { 2 } = 20 y$
E)​ $y = \frac { 1 } { 5 } x ^ { 2 }$

Question 31

Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 9 } { 2 } x$

A)vertex: (0,0)focus: $$\left( - \frac { 9 } { 8 } , 0 \right)$$
B)vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( - \frac { 9 } { 2 } , - \frac { 9 } { 2 } \right)$
C)vertex: (0,0)focus: $\left( 0 , - \frac { 9 } { 2 } \right)$
D)vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $$\left( 0 , - \frac { 9 } { 8 } \right)$$
E)vertex: (0,0)focus: $\left( - \frac { 9 } { 2 } , 0 \right)$

Question 32

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Focies: (±7,0);major axis of length 16
​

A) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 15 } = 1$
B) $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 15 } = 1$
C) $- \frac { x ^ { 2 } } { 15 } + \frac { y ^ { 2 } } { 64 } = 1$
D) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 15 } = - 1$
E) $\frac { x ^ { 2 } } { 15 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 33

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 20 feet and a height at the center of 4 feet.Select the arch of the tunnel on a rectangular coordinate system with the center of the road entering the tunnel at the origin.Identify the coordinates of the known points. ​

A)​
B)​
C)​
D)​
E)​

Question 34

Identify the conic.​ $4 y ^ { 2 } - 8 x = 0$ ​

A)Circle
B)Ellipse
C)Parabola
D)Hyperbola
E)Line

Question 35

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

A) $$x ^ { 2 } = - 4 y$$ ,focus: $\left( 0 , - \frac { 1 } { 4 } \right)$
B) $x ^ { 2 } = - \frac { 1 } { 16 } y$ ,focus: $\left( 0 , - \frac { 1 } { 16 } \right)$
C) $x ^ { 2 } = - \frac { 1 } { 4 } y$ ,focus: $\left( 0 , - \frac { 1 } { 16 } \right)$
D) $x ^ { 2 } = - 4 y$ ,focus: (0,-4)
E) $x ^ { 2 } = - \frac { 1 } { 4 } y$ ,focus: $\left( 0 , - \frac { 1 } { 4 } \right)$

Question 36

Identify the conic.​ $4 y ^ { 2 } - 3 x ^ { 2 } + 12 = 0$ ​

A)Circle
B)Ellipse
C)Hyperbola
D)Parabola
E)Line

Question 37

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (0,±5);focies: (0,±6)
​

A) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 11 } = - 1$
B) $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = 1$
C) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 11 } = 1$
D) $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = - 1$
E) $- \frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 11 } = - 1$

Question 38

Match the equation with its graph. $x ^ { 2 } + 4 y ^ { 2 } = 4$

A)
B)
C) ​
D)
E) ​

Question 39

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Vertices: (0,±7);focies: (0,±4)
​

A) $$\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$$
B) $$\frac { x ^ { 2 } } { 33 } + \frac { y ^ { 2 } } { 49 } = 1$$
C) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = - 1$
D) $- \frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$
E) $\frac { x ^ { 2 } } { 33 } + \frac { y ^ { 2 } } { 49 } = - 1$

Question 40

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (0,±2);asymptotes: y = ± $\frac { 3 } { 2 }$ x
​

A) $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 4 } = 1$
B) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$
C) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 4 } = - 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$
E) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 4 } = 1$

Question 41

Find the standard form of the equation of the hyperbola with the given characteristics. focies: (±4,0),asymptotes: $y = \pm 5 x$

A) $\frac { x ^ { 2 } } { \frac { 1 } { 26 } } - \frac { y ^ { 2 } } { \frac { 1 } { 26 } } = 1$
B) $\frac { x ^ { 2 } } { \frac { 8 } { 13 } } - \frac { y ^ { 2 } } { \frac { 200 } { 13 } } = 1$
C) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 16 } = 1$
D) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 400 } = 1$
E) $\frac { x ^ { 2 } } { \frac { 200 } { 13 } } - \frac { y ^ { 2 } } { \frac { 8 } { 13 } } = 1$

Question 42

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0,±4)focies: (0,±5)

A) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$
B) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$
C) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1$
D) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 25$
E) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 25 } = 1$

Question 43

Find the standard form of the equation of the ellipse with the following graph.

A) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 0$ , $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 0$ , $x ^ { 2 } + \frac { y ^ { 2 } } { 16 } = 0$
B) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 100$ , $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$ , $x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1$
C) $25 x ^ { 2 } + 4 y ^ { 2 } = 1$ , $\frac { x ^ { 2 } } { 2 } - \frac { y ^ { 2 } } { 36 } = 1$ , $\frac { x ^ { 2 } } { 16 } - y ^ { 2 } = 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$ , $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 1$ , $x ^ { 2 } + \frac { y ^ { 2 } } { 16 } = 1$
E) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } = 1$ , $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 36 } = 1$ , $\frac { x ^ { 2 } } { 16 } + y ^ { 2 } = 1$

Question 44

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( 0 , \frac { 1 } { 2 } \right)$

A) $x ^ { 2 } = \frac { 2 } { 4 } y$
B) $y ^ { 2 } = \frac { 2 } { 4 } x$
C) $y ^ { 2 } = \frac { 4 } { 2 } x$
D) $x ^ { 2 } = \frac { 4 } { 2 } y$
E) $y ^ { 2 } = x$

Question 45

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Vertical axis and passes through the point (6,8)
​

A) $x ^ { 2 } = \frac { 36 } { 8 } y$
B) $y ^ { 2 } = \frac { 8 } { 36 } x$
C) $x ^ { 2 } = \frac { 8 } { 36 } y$
D) $y ^ { 2 } = x$
E)​ $y ^ { 2 } = \frac { 36 } { 8 } x$

Question 46

Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance)shown in the picture. ​ d = 2.25 inches

A) $x ^ { 2 } = 9 y$
B)​ $y ^ { 2 } = \frac { 1 } { 9 } x$
C)​ $x ^ { 2 } = 2.25 y$
D)​ $y ^ { 2 } = 2.25 x$
E) $y ^ { 2 } = 9 x$

Question 47

Find the center and the vertices which located on the major axis of the ellipse. $81 x ^ { 2 } + y ^ { 2 } = 81$

A)center: (0,0)vertices: (-9,0), (9,0)
B)center: (0,0)vertices: (0,-9), (0,9)
C)center: (-9,9)vertices: (-1,0), (1,0)
D)center: (0,0)vertices: (-9,-1), (9,1)
E)center: (-9,9)vertices: (-1,-9), (1,9)

Question 48

Select the graph of the following equation.​ $$x ^ { 2 } = 8 y$$ ​

A)​
B)​
C)​
D)​
E)​

Question 49

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( 0 , - 4 )$

A) $x ^ { 2 } = 16 y$
B) $y ^ { 2 } = x$
C) $y ^ { 2 } = 16 x$
D) $x ^ { 2 } = - 16 y$
E) $y ^ { 2 } = - 16 x$

Question 50

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( - 3,0 )$

A) $x ^ { 2 } = y$
B) $y ^ { 2 } = 12 x$
C) $y ^ { 2 } = - 12 x$
D) $x ^ { 2 } = 12 y$
E) $x ^ { 2 } = - 12 y$

Question 51

Find the standard form of the equation of the ellipse with the following characteristics. focies: (±8,0)major axis of length: 22

A) $$\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 64 } = 1$$
B)​ $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 64 } = 1$
C) $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 57 } = 1$
D) $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 420 } = 1$
E) $$\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 121 } = 1$$

Question 52

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Directrix: $y = 3$ ​

A) $y ^ { 2 } = - 12 x$
B) $y ^ { 2 } = x$
C) $y ^ { 2 } = 12 x$
D) $x ^ { 2 } = 12 y$
E) $x ^ { 2 } = - 12 y$

Question 53

Sketch the graph of the ellipse,using the lateral recta.​ $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$ ​

A)​
B)​
C)​
D)​
E)​

Question 54

Select the graph of the following equation: ​​ $$y ^ { 2 } = - 2 x$$

A)​
B)​
C)​
D)​
E)​

Question 55

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Directrix: $x = - 6$ ​

A) $y ^ { 2 } = 24 x$
B) $y ^ { 2 } = x$
C) $y ^ { 2 } = - 24 x$
D) $x ^ { 2 } = 24 y$
E) $x ^ { 2 } = - 24 y$

Question 56

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Vertical axis and passes through the point (-8,-8)
​

A) $y ^ { 2 } = - 8 x$
B) $y ^ { 2 } = x$
C) $x ^ { 2 } = - 8 y$
D) $x ^ { 2 } = 8 y$
E) $y ^ { 2 } = 8 x$

Question 57

Find the vertices and asymptotes of the hyperbola. $25 y ^ { 2 } - 4 x ^ { 2 } = 100$

A)vertices: (±2,0),asymptote: $$y = \pm \frac { 5 } { 2 } x$$
B)vertices: (0,±2),asymptote: $y = \pm \frac { 2 } { 5 } x$
C)vertices: (±2,0),asymptote: $$y = \pm \frac { 2 } { 5 } x$$
D)vertices: (0,±2),asymptote: $y = \pm \frac { 5 } { 2 } x$
E)vertices: (±2,5),asymptote: $y = \pm \frac { 2 } { 5 } x$

Question 58

Find the center and vertices which located on the major axis of the ellipse. $$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$$

A)center: (0,0)vertices: (0,-5), (0,5)
B)center: (0,0)vertices: (-3,0), (3,0)
C)center: (5,3)vertices: (-5,-3), (5,3)
D)center: (0,0)vertices: (-5,0), (5,0)
E)center: (5,0)vertices: (0,-3), (0,3)

Question 59

Sketch the graph of the ellipse,using the lateral recta.​ $$16 x ^ { 2 } + 4 y ^ { 2 } = 64$$ ​

A)​
B)​
C)​
D)​
E)​

Question 60

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$ ​

A) $y ^ { 2 } = - \frac { 28 } { 2 } x$
B) $x ^ { 2 } = \frac { 2 } { 28 } y$
C) $y ^ { 2 } = - \frac { 2 } { 28 } x$
D) $x ^ { 2 } = - \frac { 2 } { 28 } y$
E) $y ^ { 2 } = \frac { 2 } { 28 } x$

Question 61

Find the standard form of the equation of the parabola with the given characteristics. ​
Vertex: $( 1,2 )$ ;directrix: $y = - 2$ ​

A) $( y - 1 ) ^ { 2 } = 2 ( x - 2 )$
B) $( x - 1 ) ^ { 2 } = - 16 ( y - 2 )$
C) $( y - 1 ) ^ { 2 } = - 16 ( x - 2 )$
D) $( x - 1 ) ^ { 2 } = 2 ( y - 2 )$
E) $( x - 1 ) ^ { 2 } = 16 ( y - 2 )$

Question 62

Find the standard form of the equation of the parabola with the given characteristics. ​
Vertex: $( - 5,5 )$ ;focus: $( - 5,0 )$ ​

A) $( x - 5 ) ^ { 2 } = 20 ( y - 5 )$
B) $( x - 5 ) ^ { 2 } = - 20 ( y - 5 )$
C) $( y - 5 ) ^ { 2 } = - 20 ( x - 5 )$
D) $( y - 5 ) ^ { 2 } = 20 ( x - 5 )$
E) $( x + 5 ) ^ { 2 } = - 20 ( y - 5 )$

Question 63

Find the vertex,focus,and directrix of the parabola.​ $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )$ ​

A)Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ;Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ;Directrix: $y = 0$
B)Vertex: $\left( - \frac { 7 } { 2 } , 2 \right)$ ;Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ;Directrix: $y = 1$
C)Vertex: $\left( - \frac { 7 } { 2 } , 2 \right)$ ;Focus: $\left( - \frac { 7 } { 2 } , 1 \right)$ ;Directrix: $y = 0$
D)Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ;Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ;Directrix: $y = 1$
E)Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ;Focus: $\left( - \frac { 7 } { 2 } , 1 \right)$ ;Directrix: $y = 1$

Question 64

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. ​
Parabola: $y ^ { 2 } - 24 x = 0$ Tangent Line: $x - y + 6 = 0$ ​

A)​
B)​
C)​
D)​
E)​

Question 65

Find the equation of the parabola so that its graph matches the description.​ $( y - 5 ) ^ { 2 } = 2 ( x + 1 )$ ;upper half of parabola ​

A) $x = \sqrt { 2 ( y + 1 ) } + 5$
B) $x = - \sqrt { 2 ( y + 1 ) } + 5$
C) $y = \sqrt { 2 ( x - 1 ) } + 5$
D) $y = \sqrt { 2 ( x + 1 ) } + 5$
E) $y = - \sqrt { 2 ( x + 1 ) } + 5$

Question 66

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Horizontal axis and passes through the point $( 3 , - 2 )$ ​

A) $y ^ { 2 } = x$
B) $y ^ { 2 } = \frac { 4 } { 3 } x$
C) $y ^ { 2 } = \frac { 3 } { 4 } x$
D) $x ^ { 2 } = \frac { 4 } { 3 } y$
E) $x ^ { 2 } = \frac { 3 } { 4 } y$

Question 67

Find the vertex,focus,and directrix of the parabola.​ $y ^ { 2 } = - 3 x$ ​

A)Vertex: (0,0);Focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 3 } { 4 }$
B)Vertex: (0,0);Focus: $\left( - \frac { 1 } { 3 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 3 }$
C)Vertex: (0,0);Focus: $\left( \frac { 1 } { 3 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 3 }$
D)Vertex: (0,0);Focus: $\left( \frac { 3 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 3 } { 4 }$
E)Vertex: (0,0);Focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ ;Directrix: $x = \frac { 3 } { 4 }$

Question 68

Find the equation of the parabola so that its graph matches the description.​ $( y + 2 ) ^ { 2 } = 3 ( x - 7 )$ ;lower half of parabola ​

A) $y = - 2 + \sqrt { 3 ( x - 7 ) }$
B) $y = - 2 - \sqrt { 3 ( x - 7 ) }$
C) $x = - 2 + \sqrt { 3 ( y - 7 ) }$
D) $x = - 2 - \sqrt { 3 ( y - 7 ) }$
E) $x = - 2 + \sqrt { 3 ( y + 7 ) }$

Question 69

Find the vertex,focus,and directrix of the parabola.​ $x ^ { 2 } + 4 y = 0$ ​

A)Vertex: (0,0);Focus: $\left( \frac { 1 } { 4 } , 0 \right)$ ;Directrix: $y = \frac { 1 } { 4 }$
B)Vertex: (0,0);Focus: $\left( - \frac { 1 } { 4 } , 0 \right)$ ;Directrix: $y = \frac { 1 } { 4 }$
C)Vertex: (0,0): Focus: $\left( 0 , \frac { 4 } { 4 } \right)$ Directrix: $y = - \frac { 4 } { 4 }$
D)Vertex: (0,0);Focus: $\left( 0 , - \frac { 4 } { 4 } \right)$ ;Directrix: $y = \frac { 4 } { 4 }$
E)Vertex: (0,0);Focus: $\left( 0 , - \frac { 4 } { 4 } \right)$ ;Directrix: $y = - \frac { 4 } { 4 }$

Question 70

Find the vertex,focus,and directrix of the parabola.​ $( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)$ ​

A)Vertex: $\left( - 5 , \frac { 5 } { 2 } \right)$ ;Focus: $\left( - 5 , \frac { 7 } { 2 } \right)$ ;Directrix: $y = \frac { 3 } { 2 }$
B)Vertex: $\left( \frac { 5 } { 2 } , - 5 \right)$ ;Focus: $\left( - 5 , \frac { 3 } { 2 } \right)$ ;Directrix: $y = \frac { 3 } { 2 }$
C)Vertex: $\left( \frac { 5 } { 2 } , - 5 \right)$ ;Focus: $\left( - 5 , \frac { 7 } { 2 } \right)$ ;Directrix: $y = \frac { 3 } { 2 }$
D)Vertex: $\left( - 5 , \frac { 5 } { 2 } \right)$ ;Focus: $\left( - 5 , \frac { 3 } { 2 } \right)$ ;Directrix: $y = \frac { 7 } { 2 }$
E)Vertex: $( 0,0 )$ ;Focus: $\left( - 5 , \frac { 7 } { 2 } \right)$ ;Directrix: $y = \frac { 7 } { 2 }$

Question 71

Find the vertex,focus,and directrix of the parabola.​ $y = - 3 x ^ { 2 }$ ​

A)Vertex: (0,0);Focus: $\left( 0 , - \frac { 1 } { 12 } \right)$ ;Directrix: $y = - \frac { 1 } { 12 }$
B)Vertex:(0,0);Focus: $\left( 0 , - \frac { 1 } { 12 } \right)$ ;Directrix: $y = \frac { 1 } { 12 }$
C)Vertex: (0,0);Focus: $\left( 0 , \frac { 1 } { 3 } \right)$ ;Directrix: $y = \frac { 1 } { 3 }$
D)Vertex: (0,0);Focus: $\left( 0 , \frac { 1 } { 12 } \right)$ ;Directrix: $y = \frac { 1 } { 12 }$
E)Vertex: (0,0);Focus: $\left( 0 , - \frac { 1 } { 3 } \right)$ ;Directrix: $y = \frac { 1 } { 3 }$

Question 72

Find the vertex,focus,and directrix of the parabola.​ $( x - 1 ) ^ { 2 } + 16 ( y + 6 ) = 0$ ​

A)Vertex: $( 0 , - 4 )$ ;Focus: $( 1 , - 6 )$ ;Directrix: $y = 0$
B)Vertex: $( 1 , - 10 )$ ;Focus: $( 1 , - 10 )$ ;Directrix: $y = 0$
C)Vertex: $( - 4,1 )$ ;Focus: $( - 4,1 )$ ;Directrix: $y = 0$
D)Vertex: $( 1 , - 6 )$ ;Focus: $( 1 , - 10 )$ ;Directrix: $y = 0$
E)Vertex: $( 1 , - 6 )$ ;Focus: $( 1 , - 4 )$ ;Directrix: $y = 6$

Question 73

Find the standard form of the equation of the parabola with the given characteristics. ​
Vertex: $( 0,2 )$ ;directrix: $y = 10$ ​

A) $x ^ { 2 } = - 32 ( y - 10 )$
B) $y ^ { 2 } = - 32 ( x - 2 )$
C) $x ^ { 2 } = 32 ( y - 2 )$
D) $y ^ { 2 } = 32 ( x - 2 )$
E) $x ^ { 2 } = - 32 ( y - 2 )$

Question 74

Find the vertex,focus,and directrix of the parabola.​ $y ^ { 2 } = 10 x$ ​

A)Vertex: (0,0);Focus: $\left( \frac { 10 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 10 } { 4 }$
B)Vertex: (0,0);Focus: $\left( \frac { 1 } { 10 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 10 }$
C)Vertex: (0,0);Focus: $\left( - \frac { 10 } { 4 } , 0 \right)$ ;Directrix: $x = - \frac { 10 } { 4 }$
D)Vertex: (0,0);Focus: $\left( - \frac { 10 } { 4 } , 0 \right)$ ;Directrix: $x = \frac { 10 } { 4 }$
E)Vertex: (0,0);Focus: $\left( - \frac { 1 } { 10 } , 0 \right)$ ;Directrix: $x = \frac { 1 } { 10 }$

Question 75

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. ​
Parabola: $$x ^ { 2 } + 20 y = 0$$ Tangent Line: $$x + y - 5 = 0$$ ​

A)​
B)​
C)​
D)​
E)​

Question 76

Find the vertex,focus,and directrix of the parabola.​ $( x + 3 ) + ( y - 1 ) ^ { 2 } = 0$ ​

A)Vertex: $( - 3,1 )$ ;Focus: $\left( \frac { - 13 } { 4 } , 1 \right)$ ;Directrix: $x = \frac { - 11 } { 4 }$
B)Vertex: $( 1 , - 3 , )$ ;Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$
C)Vertex: $( 1 , - 3 , )$ ;Focus: $\left( \frac { - 11 } { 4 } , 1 \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$
D)Vertex: $( - 3,1 )$ ;Focus: $\left( 1 , \frac { - 13 } { 4 } \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$
E)Vertex: $( - 3,1 )$ ;Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ;Directrix: $x = \frac { - 13 } { 4 }$

Question 77

The revenue R (in dollars)generated by the sale of x units of a patio furniture set is given by $$( x - 112 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 12544 )$$ .Select the correct graph of the function. ​

A)​
B)​
C)​ .
D)​
E)​

Question 78

Find the standard form of the equation of the parabola with the given characteristics. ​
Vertex: $( 6,5 )$ ;focus: $( 8,5 )$ ​

A) $( y - 6 ) ^ { 2 } = 8 ( x - 5 )$
B) $( y - 5 ) ^ { 2 } = 8 ( x - 6 )$
C) $( x - 6 ) ^ { 2 } = - 8 ( y - 5 )$
D) $( y - 6 ) ^ { 2 } = - 8 ( x - 5 )$
E) $( x - 5 ) ^ { 2 } = 8 ( y - 6 )$

Question 79

The revenue R (in dollars)generated by the sale of x units of a patio furniture set is given by $( x - 116 ) ^ { 2 } = - \frac { 4 } { 5 } ( R - 16,820 )$ .Approximate the number of sales that will maximize revenue. ​

A) $$R = 116 x - \frac { 5 } { 4 } x ^ { 2 }$$ The revenue is maximum when $x = 116$ units.
B) $R = 116 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 16,820$ units.
C) $R = 290 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 16,820$ units.
D) $R = 290 x - \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 116$ units.
E) $R = 290 x + \frac { 5 } { 4 } x ^ { 2 }$ The revenue is maximum when $x = 290$ units.

Question 80

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Horizontal axis and passes through the point $( - 4,7 )$ ​

A) $x ^ { 2 } = \frac { - 4 } { 49 } y$
B) $y ^ { 2 } = \frac { - 4 } { 49 } x$
C) $y ^ { 2 } = \frac { 49 } { - 4 } x$
D) $x ^ { 2 } = \frac { 49 } { - 4 } y$
E) $y ^ { 2 } = x$