Question 1

In a suspension bridge, the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 400 m apart, and the lowest point of the suspension cables is 100 m below the top of the towers. Find the equation of the parabolic part of the cables, placing the origin of the coordinate system at the lowest point of the cable. NOTE: This equation is used to find the length of the cable needed in the construction of the bridge. A) x² = 800y B) x² = 400y C) x² = -400y D) x² = 1,600y E) y² = 1,600x

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Question 2

Find the graph of the following ellipse. 
A) 
B) 
C) 
D)

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Question 3

Identify the graph of the following ellipse. 
A) 
B) 
C)

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Question 4

Find the equation of the circle graphed below. 
A) 
B) 
C) 
D) 
E)

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Question 5

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (-6, -2), (-2, -2)
Asymptotes: 
A) 
B) 
C) 
D) 
E)

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Question 6

Write the equation of the ellipse that has its center at the origin, focus at (2, 0) and vertex at (7, 0).
A) 
B) 
C) 
D) 
E)

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Question 7

Write the equation of the ellipse that has its center at the origin with focus at (0, 5) and vertex at (0, 10).
A) 
B) 
C) 
D) 
E) none of these

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Question 8

Give the coordinates of the circle's center and its radius. 
A) (9, -6); r = 16
B) (9, -6); r = 4
C) (-9, 6); r = 4
D) (-9, 6); r = 16
E) none of these

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Question 9

Find the center and vertices of the ellipse. 
A) center:  vertices:

B) center:  vertices:

C) center:  vertices:

D) center:  vertices:

E) center:  vertices:

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Question 10

Graph the following equation. 
A) 
B) 
C)

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A) 
B) 
C)...

Question 11

Any sound from one focus of an ellipse reflects off the ellipse directly back to the other focus. This property explains whispering galleries such as Statuary Hall in Washington, D.C. The whispering gallery shown in illustration has the shape of a semi-ellipse. Find the distance sound travels as it leaves focus F and returns to focus F'. 
A) 63.2 meters
B) 33.5 meters
C) 31.6 meters
D) 32 meters
E) 31 meters

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Question 12

Write the equation of the ellipse with foci at (4, 2), (6, 2), and b = 2.
A) 
B) 
C) 
D) 
E)

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Question 13

Find the standard form of the equation of the ellipse with vertices  and eccentricity  .
A) 
B) 
C) 
D) 
E)

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Question 14

Graph the hyperbola. 
A) 
B) 
C) 
D)

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A) 
B) 
C) 
D)...

Question 15

Give the coordinates of the circle's center and its radius. 
A) (0, 0); r = 144
B) (0, 0); r = 12
C) (1, 1); r = 144
D) (1, 1); r = 12
E) none of these

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Question 16

Find the standard form of the equation of the hyperbola with the given characteristics. vertices:  foci: 
A) 
B) 
C) 
D) 
E)

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Question 17

Find the equation of the parabola with vertex at (3, 4) and focus at (-4, 4).
A) 
B) 
C) 
D) 
E)

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Question 18

Find the vertex and directrix of the parabola. 
A) vertex:  directrix:

B) vertex:  directrix:

C) vertex:  directrix:

D) vertex:  directrix:

E) vertex:  directrix:

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Question 19

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 4).
A) 
B) 
C) 
D) 
E) none of these

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Question 20

Find the vertices and asymptotes of the hyperbola. 
A) vertices:  asymptote:

B) vertices:  asymptote:

C) vertices:  asymptote:

D) vertices:  asymptote:

E) vertices:  asymptote:

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Quiz 10: Topics in Analytic Geometry

Find the graph of the following ellipse.

Identify the graph of the following ellipse.

Find the equation of the circle graphed below.

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (-6, -2) , (-2, -2) Asymptotes:

Write the equation of the ellipse that has its center at the origin, focus at (2, 0) and vertex at (7, 0) .

Write the equation of the ellipse that has its center at the origin with focus at (0, 5) and vertex at (0, 10) .

Give the coordinates of the circle's center and its radius.

Find the center and vertices of the ellipse.

Graph the following equation.

Write the equation of the ellipse with foci at (4, 2) , (6, 2) , and b = 2.

Find the standard form of the equation of the ellipse with vertices and eccentricity .

Graph the hyperbola.

Give the coordinates of the circle's center and its radius.

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: foci:

Find the equation of the parabola with vertex at (3, 4) and focus at (-4, 4) .

Find the vertex and directrix of the parabola.

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 4) .

Find the vertices and asymptotes of the hyperbola.