Question 1

Identify the conic by writing the equation in standard form.

Accepted Answer

A)    ; ellipse 
B)    ; ellipse 
C)    ; ellipse 
D)    ; ellipse 
E)    ; circle 
A)    ; ellipse 
B)    ; ellipse 
C)    ; ellipse 
D)    ; ellipse 
E)    ; circle

Question 2

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Find the center and vertices of the hyperbola.

Accepted Answer

A)  center: (1, -5), vertices: (1, -10), (1, 0) 
B)  center: (-1, 5), vertices: (-1, 0), (-1, 10) 
C)  center: (-1, 5), vertices: (-6, 5), (4,5) 
D)  center: (1,-5), vertices: (-4, -5), (6, -5) 
E)  center: (-5, 1), vertices: (-10, 1), (0, 1) 
A)  center: (1, -5), vertices: (1, -10), (1, 0) 
B)  center: (-1, 5), vertices: (-1, 0), (-1, 10) 
C)  center: (-1, 5), vertices: (-6, 5), (4,5) 
D)  center: (1,-5), vertices: (-4, -5), (6, -5) 
E)  center: (-5, 1), vertices: (-10, 1), (0, 1)

Question 4

Identify the conic by writing the equation in standard form.

Accepted Answer

A)    ; ellipse 
B)    ; ellipse 
C)    ; ellipse 
D)    ; ellipse 
E)    ; circle 
A)    ; ellipse 
B)    ; ellipse 
C)    ; ellipse 
D)    ; ellipse 
E)    ; circle

Question 5

Find the vertices and asymptotes of the hyperbola.

Accepted Answer

A)  vertices:   asymptote:
  
B)  vertices:   asymptote:
  
C)  vertices:   asymptote:
  
D)  vertices:   asymptote:
  
E)  vertices:   asymptote:
  
A)  vertices:   asymptote:
  
B)  vertices:   asymptote:
  
C)  vertices:   asymptote:
  
D)  vertices:   asymptote:
  
E)  vertices:   asymptote:

Question 6

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

Accepted Answer

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

Question 7

Graph the hyperbola.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 8

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 3).

Accepted Answer

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

Question 9

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'.

Accepted Answer

A)  63.2 meters 
B)  33.5 meters 
C)  31.6 meters 
D)  32 meters 
E)  31 meters 
A)  63.2 meters 
B)  33.5 meters 
C)  31.6 meters 
D)  32 meters 
E)  31 meters

Question 10

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

In a suspension bridge, the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 1000 m apart, and the lowest point of the suspension cables is 200 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.

Accepted Answer

A)  x 2 = -1,250y 
B)  x 2 = 1,250y 
C)  x 2 = 5,000y 
D)  x 2 = 2,500y 
E)  y 2 = 5,000x 
A)  x 2 = -1,250y 
B)  x 2 = 1,250y 
C)  x 2 = 5,000y 
D)  x 2 = 2,500y 
E)  y 2 = 5,000x

Question 12

Find the vertices and asymptotes of the hyperbola.

Accepted Answer

A)  vertices:   asymptote:
  
B)  vertices:   asymptote:
  
C)  vertices:   asymptote:
  
D)  vertices:   asymptote:
  
E)  vertices:   asymptote:
  
A)  vertices:   asymptote:
  
B)  vertices:   asymptote:
  
C)  vertices:   asymptote:
  
D)  vertices:   asymptote:
  
E)  vertices:   asymptote:

Question 13

Graph the hyperbola.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Find the center and vertices of the ellipse.   = 0

Accepted Answer

A)  center: (8, 7) vertices: (6, 7), (10, 7) 
B)  center: (8, 7) vertices: (7, 7), (9, 7) 
C)  center: (-8, -7) vertices: (-10, -7), (-6, -7) 
D)  center: (7, 8) vertices: (5, 8), (9, 8) 
E)  center: (-8, -7) vertices: (-9, -7), (-7, -7) 
A)  center: (8, 7) vertices: (6, 7), (10, 7) 
B)  center: (8, 7) vertices: (7, 7), (9, 7) 
C)  center: (-8, -7) vertices: (-10, -7), (-6, -7) 
D)  center: (7, 8) vertices: (5, 8), (9, 8) 
E)  center: (-8, -7) vertices: (-9, -7), (-7, -7)

Question 18

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

Accepted Answer

A)  (9, -6); r = 16 
B)  (9, -6); r = 4 
C)  (-9, 6); r = 4 
D)  (-9, 6); r = 16 
E)  none of these 
A)  (9, -6); r = 16 
B)  (9, -6); r = 4 
C)  (-9, 6); r = 4 
D)  (-9, 6); r = 16 
E)  none of these

Question 19

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Identify the conic by writing the equation in standard form.

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

Find the center and vertices of the hyperbola.

Identify the conic by writing the equation in standard form.

Find the vertices and asymptotes of the hyperbola.

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

Graph the hyperbola.

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 3).

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

Find the vertices and asymptotes of the hyperbola.

Graph the hyperbola.

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

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

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

Find the center and vertices of the ellipse. = 0

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

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

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

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Prerequisites

Filters

Exam 10: Topics in Analytic Geometry

Identify the conic by writing the equation in standard form.

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

Find the center and vertices of the hyperbola.

Identify the conic by writing the equation in standard form.

Find the vertices and asymptotes of the hyperbola.

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

Graph the hyperbola.

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 3).

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

Find the vertices and asymptotes of the hyperbola.

Graph the hyperbola.

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

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

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

Find the center and vertices of the ellipse. = 0

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

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

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

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Prerequisites

Filters