Question 1

Use the following to answer questions :
y = 2xS1U1P12S1S1P0 - x - 3
-Find the x- and y-intercepts (if they exist).
A) x-intercepts:  ; y-intercept: (0, 3)
B) x-intercepts:  ; y-intercept: (0, -3)
C) x-intercepts:  ; y-intercept: (0, -3)
D) x-intercepts: none; y-intercept: (0, -3)

Accepted Answer

The answer of Use the following to answer questions :
y...

Question 2

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 4x² + 9y² - 40x - 18y = -73 A) Circle B) Ellipse C) Hyperbola D) None of these

Accepted Answer

The equation can be rearranged to:
4(x-5)^2 + 9(y-2)^2 = 100
This is in the standard form of the equation for an ellipse. Therefore, the answer is B.

Question 3

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. 
A)

B)

C)

D)

Accepted Answer

The answer of Sketch a complete graph of the equation,...

Question 4

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. (x - 1)² - 9(y - 2)² = 9

Accepted Answer

The answer of Sketch a complete graph of the equation,...

Question 5

Use the following to answer questions :
y = xS1U1P12S1S1P0 - 4x + 3
-Find the vertex.

Accepted Answer

The answer of Use the following to answer questions :
y...

Question 6

Graph the hyperbola. Label the vertices.

Accepted Answer

The answer of Graph the hyperbola. Label the vertices. ...

Question 7

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

Accepted Answer

The answer of Sketch a complete graph of the equation,...

Question 8

For the graph given, state the location of the vertices, the equation of the transverse axis, the location of the center, and the equation of the conjugate axis.  (Gridlines are spaced one unit apart.)
A) vertices: (1, 2), (1, 4); transverse axis: x = 3; center (1, 3); conjugate axis: y = 1
B) vertices: (1, 2), (1, 4); transverse axis: y = 3; center (1, 3); conjugate axis: x = 1
C) vertices: (1, 2), (1, 4); transverse axis: x = 1; center (1, 3); conjugate axis: y = 3
D) vertices: (1, 2), (1, 4); transverse axis: y = 1; center (1, 3); conjugate axis: x = 3

Accepted Answer

The transverse axis of the graph is horizontal and passes through the points (1,2) and (1,4). This means that the center of the graph must be at (1,3) since that is the midpoint of the vertices.

The length of the transverse axis is the difference in the x-coordinates of the vertices, which is 0. Therefore, the equation of the transverse axis is x=1.

The conjugate axis is vertical and runs through the center, with a length equal to the difference in the y-coordinates of the vertices. This length is 2, so the equation of the conjugate axis is y=3±1. Since the center is at (1,3), the equation of the conjugate axis is y=3±1, or y=2 and y=4.

Therefore, the correct answer is C.

Question 9

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 9x² + 9y² - 18x + 72y + 72 = 0 A) Circle B) Ellipse C) Hyperbola D) None of these

Accepted Answer

The equation simplifies to $9x^2 + 9y^2 - 18x + 72y + 72 = 0$. By completing the square for both x and y terms, we can rewrite it in the standard form of a circle, indicating it represents a circle.

Question 10

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 4x² - 7y² = 28 A) Circle B) Ellipse C) Hyperbola D) None of these

Accepted Answer

The equation 4x^2 - 7y^2 = 28 is of the form Ax^2 - By^2 = C, which is the standard form of a hyperbola.

Question 11

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. 
A)

B)

C)

D)

Accepted Answer

The equation appears to be for a hyperbola, and Choice C shows a hyperbola with a center at (-2,3), vertices at (-9,3) and  (5,3), and asymptotes at y=3±2/3(x+2). All other choices are either circles or ellipses, or do not have the correct center and vertices.

Question 12

For the graph given, state
(a) the location of the vertices
(b) the equation of the transverse axis
(c) the location of the center
(d) the equation of the conjugate axis
Assume all coordinates are lattice points.  (Gridlines are spaced one unit apart.)

Accepted Answer

The answer of For the graph given, state
(a) the location...

Question 13

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. x² - 9y² - 6x - 36y - 36 = 0

Accepted Answer

The answer of Sketch a complete graph of the equation,...

Question 14

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

Accepted Answer

The answer of Sketch a complete graph of the equation,...

Question 15

Graph the hyperbola. Label the vertices. 
A)

(Gridlines are spaced one unit apart.)
B)

(Gridlines are spaced one unit apart.)
C)

(Gridlines are spaced one unit apart.)
D)

(Gridlines are spaced one unit apart.)

Accepted Answer

The hyperbola has a horizontal transverse axis and a center at (-2,2). The distance from the center to each vertex is 3 units, so the vertices are located at (-5,2) and (1,2). Option C is the only graph that satisfies these conditions.

Question 16

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 9x² = -49y² + 441 A) Circle B) Ellipse C) Hyperbola D) None of these

Accepted Answer

The answer of Classify the equation as that of a...

Question 17

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. 25y² - 4x² = 100

Accepted Answer

The answer of Sketch a complete graph of the equation,...

Question 18

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 8y² - 4 = 5x² + 36 A) Circle B) Ellipse C) Hyperbola D) None of these

Accepted Answer

The equation can be rewritten as 8y^2 - 5x^2 = 40, which is in the standard form of a hyperbola (Ax^2 - By^2 = C) where A and B are positive constants.

Question 19

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. -2x² + -2y²= -20 A) Circle B) Ellipse C) Hyperbola D) None of these

Accepted Answer

The equation can be written in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2 where (h, k) is the center of the circle and r is the radius. Dividing both sides by -20, we get: x^2 + y^2 = (1/10)(²) This is in the standard form of a circle, with center (0,0) and radius equal to the square root of (1/10)(²). Therefore, the equation is that of a circle.

Question 20

Use the following to answer questions :
y = xS1U1P12S1S1P0 - 4x + 3
-Find the x- and y-intercepts (if they exist).

Accepted Answer

The answer of Use the following to answer questions :
y...

Quiz 9: Analytical Geometry

Use the following to answer questions : y = 2x² - x - 3 -Find the x- and y-intercepts (if they exist) .

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 4x² + 9y² - 40x - 18y = -73

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. (x - 1)² - 9(y - 2)² = 9

Use the following to answer questions : y = x² - 4x + 3 -Find the vertex.

Graph the hyperbola. Label the vertices.

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

For the graph given, state the location of the vertices, the equation of the transverse axis, the location of the center, and the equation of the conjugate axis. (Gridlines are spaced one unit apart.)

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 9x² + 9y² - 18x + 72y + 72 = 0

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 4x² - 7y² = 28

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

For the graph given, state (a) the location of the vertices (b) the equation of the transverse axis (c) the location of the center (d) the equation of the conjugate axis Assume all coordinates are lattice points. (Gridlines are spaced one unit apart.)

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. x² - 9y² - 6x - 36y - 36 = 0

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

Graph the hyperbola. Label the vertices.

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 9x² = -49y² + 441

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. 25y² - 4x² = 100

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 8y² - 4 = 5x² + 36

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. -2x² + -2y²= -20

Use the following to answer questions : y = x² - 4x + 3 -Find the x- and y-intercepts (if they exist).

Quiz 9: Analytical Geometry

Use the following to answer questions : y = 2x2 - x - 3 -Find the x- and y-intercepts (if they exist) .

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 4x2 + 9y2 - 40x - 18y = -73

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. (x - 1)2 - 9(y - 2)2 = 9

Use the following to answer questions : y = x2 - 4x + 3 -Find the vertex.

Graph the hyperbola. Label the vertices.

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

For the graph given, state the location of the vertices, the equation of the transverse axis, the location of the center, and the equation of the conjugate axis. (Gridlines are spaced one unit apart.)

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 9x2 + 9y2 - 18x + 72y + 72 = 0

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 4x2 - 7y2 = 28

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

For the graph given, state (a) the location of the vertices (b) the equation of the transverse axis (c) the location of the center (d) the equation of the conjugate axis Assume all coordinates are lattice points. (Gridlines are spaced one unit apart.)

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. x2 - 9y2 - 6x - 36y - 36 = 0

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

Graph the hyperbola. Label the vertices.

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 9x2 = -49y2 + 441

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. 25y2 - 4x2 = 100

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 8y2 - 4 = 5x2 + 36

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. -2x2 + -2y2= -20

Use the following to answer questions : y = x2 - 4x + 3 -Find the x- and y-intercepts (if they exist).

Use the following to answer questions : y = 2x² - x - 3 -Find the x- and y-intercepts (if they exist) .

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 4x² + 9y² - 40x - 18y = -73

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. (x - 1)² - 9(y - 2)² = 9

Use the following to answer questions : y = x² - 4x + 3 -Find the vertex.

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 9x² + 9y² - 18x + 72y + 72 = 0

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 4x² - 7y² = 28

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. x² - 9y² - 6x - 36y - 36 = 0

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 9x² = -49y² + 441

Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. 25y² - 4x² = 100

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 8y² - 4 = 5x² + 36

Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. -2x² + -2y²= -20

Use the following to answer questions : y = x² - 4x + 3 -Find the x- and y-intercepts (if they exist).