Deck 10: Section 1: Conics, Parametric Equations, and Polar Coordinates

Question 1

Find an equation of the hyperbola with vertices and asymptotes .

A)
B)
C)
D)
E)

Answer 1

Question 2

Find the center, foci, and vertices of the hyperbola.

A)
B)
C)
D)
E)

Answer 2

Question 3

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

A) circle
B) hyperbola
C) ellipse
D) parabola

Answer 3

hyperbola

Question 4

Find the vertices of the ellipse given by .

A)
B)
C)
D)
E)

Question 5

Find an equation of the hyperbola with vertices and asymptotes .

A)
B)
C)
D)
E)

Question 6

Match the equation with its graph.

A)
B)
C)
D)
E)

Question 7

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

A) parabola
B) ellipse
C) circle
D) hyperbola

Question 8

Find an equation of the parabola with vertex and directrix .

A)
B)
C)
D)
E)

Question 9

Find the center of the ellipse given by .

A)
B)
C)
D)
E)

Question 10

Match the equation with its graph.

A)
B)
C)
D)
E) none of these

Question 11

Find the focus of the parabola given by .

A)
B)
C)
D)
E)

Question 12

Match the equation with its graph.

A)
B)
C)
D)
E)

Question 13

Find an equation of the ellipse with vertices and eccentricity .

A)
B)
C)
D)
E)

Question 14

Find the foci of the ellipse given by .

A)
B)
C)
D)
E)

Question 15

Find the directrix of the parabola given by .

A)
B)
C)
D)
E)

Question 16

Find the eccentricity of the ellipse given by .

A)
B)
C)
D)
E)

Question 17

Find the vertex, focus, and directrix of the parabola and sketch its graph.

A) vertex: ; focus: ; directrix x = -1
B) vertex: ; focus: ; directrix x = 1
C) vertex: ; focus: ; directrix x = 3
D) vertex: ; focus: ; directrix x = 3
E) vertex: ; focus: ; directrix x = -1

Question 18

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

A) hyperbola
B) circle
C) ellipse
D) parabola

Question 19

Find the vertex of the parabola given by .

A)
B)
C)
D)
E)

Question 20

Match the equation with its graph.

A)
B)
C)
D)
E)

Question 21

Saturn moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 1,433,448,036 kilometers, and the eccentricity is 0.0557. Find the minimum distance (perihelion) of Saturn from the sun. Round your answer to nearest kilometer.

A) 1,462,116,997 km
B) 1,353,604,980 km
C) 1,404,779,075 km
D) 1,513,291,092 km
E) 79,843,056 km

Question 22

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

A) parabola
B) circle
C) ellipse
D) hyperbola

Question 23

Suppose a church window is bounded above by a parabola and below by the arc of a circle as shown in figure given below. Find the surface area of the window. Round your answer to three decimal places.

A) 147.477 ft²
B) 62.143 ft²
C) 81.292 ft²
D) 53.610 ft²
E) 184.590 ft²

Question 24

Suppose a cable of a suspension bridge is suspended (in the shape of a parabola) between two towers that are 240 meters apart and 40 meters above the roadway as shown in the figure given below. The cable touches the roadway midway between the towers. Find the length of the parabolic supporting cable. Round your answer to two decimal places.

A) 280.79 meters
B) 327.58 meters
C) 291.18 meters
D) 245.71 meters
E) 256.75 meters

Question 25

Earth moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 149,598,000 kilometers, and the eccentricity is 0.0167. Find the maximum distance (aphelion) of Earth from the sun. Round your answer to nearest kilometer.

A) 146,606,040 km
B) 2,498,287 km
C) 152,589,960 km
D) 152,096,287 km
E) 147,099,713 km

Question 26

Suppose a cable of a suspension bridge is suspended (in the shape of a parabola) between two towers that are 240 meters apart and 40 meters above the roadway as shown in the figure given below. The cable touches the roadway midway between the towers. Find an equation for the parabolic shape of cable.

A)
B)
C)
D)
E)