Question 1

Find the equation of the parabola with vertex at (4, 5) and focus at (-3, 5).

Accepted Answer

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

Question 2

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 1

Accepted Answer

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

Question 3

Find the vertex and directrix of the parabola.

Accepted Answer

A) vertex:   directrix:   
B) vertex:   directrix:   
C) vertex:   directrix:   
D) vertex:   directrix:   
E) vertex:   directrix:   
A) vertex:   directrix:   
B) vertex:   directrix:   
C) vertex:   directrix:   
D) vertex:   directrix:   
E) vertex:   directrix:

Question 4

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) 59.4 meters 
B) 29 meters 
C) 29.7 meters 
D) 30.3 meters 
E) 31.4 meters 
A) 59.4 meters 
B) 29 meters 
C) 29.7 meters 
D) 30.3 meters 
E) 31.4 meters

Question 5

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -3

Accepted Answer

A) y2 = 12x 
B) x2 = -3y 
C) y2 = -3x 
D) x2 = 12y 
E) x2 = -12y 
A) y2 = 12x 
B) x2 = -3y 
C) y2 = -3x 
D) x2 = 12y 
E) x2 = -12y

Question 6

Find the standard form of the equation of the ellipse with the following characteristics. foci:   major axis of length: 20

Accepted Answer

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

Question 7

Find the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (7, 0).

Accepted Answer

A)    
B)    
C)    
D)    
E) none of these0 
A)    
B)    
C)    
D)    
E) none of these0

Question 8

Identify the conic by writing the equation in standard form.

Accepted Answer

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

Question 9

Find the standard form of the equation of the ellipse with the given characteristics. foci:   endpoints of the major axis:

Accepted Answer

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

Question 10

Find the center and vertices of the hyperbola.

Accepted Answer

A) center: (3,-4), vertices: (1, -4), (5, -4) 
B) center: (-4, 3), vertices: (-6, 3), (-2, 3) 
C) center: (3, -4), vertices: (3, -6), (3, -2) 
D) center: (-3, 4), vertices: (-5, 4), (-1,4) 
E) center: (-3, 4), vertices: (-3, 2), (-3, 6) 
A) center: (3,-4), vertices: (1, -4), (5, -4) 
B) center: (-4, 3), vertices: (-6, 3), (-2, 3) 
C) center: (3, -4), vertices: (3, -6), (3, -2) 
D) center: (-3, 4), vertices: (-5, 4), (-1,4) 
E) center: (-3, 4), vertices: (-3, 2), (-3, 6)

Question 11

Identify the conic by writing the equation in standard form.

Accepted Answer

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

Question 12

Find the vertex and focus of the parabola.

Accepted Answer

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

Question 13

Graph the hyperbola.

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Find the standard form of the equation of the ellipse with the following characteristics. foci:   major axis of length: 12

Accepted Answer

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

Question 16

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 17

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, 7)

Accepted Answer

A) x2 = 28y 
B) x2 = 7y 
C) x2 = -7y 
D) y2 = 28x 
E) y2 = 7x 
A) x2 = 28y 
B) x2 = 7y 
C) x2 = -7y 
D) y2 = 28x 
E) y2 = 7x

Question 18

Find the vertex and directrix of the parabola.

Accepted Answer

A) vertex:   directrix:   
B) vertex:   directrix:   
C) vertex:   directrix:   
D) vertex:   directrix:   
E) vertex:   directrix:   
A) vertex:   directrix:   
B) vertex:   directrix:   
C) vertex:   directrix:   
D) vertex:   directrix:   
E) vertex:   directrix:

Question 19

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 20

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:

Find the equation of the parabola with vertex at (4, 5) and focus at (-3, 5).

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 1

Find the vertex and directrix of the parabola.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -3

Find the standard form of the equation of the ellipse with the following characteristics. foci: major axis of length: 20

Find the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (7, 0).

Identify the conic by writing the equation in standard form.

Find the standard form of the equation of the ellipse with the given characteristics. foci: endpoints of the major axis:

Find the center and vertices of the hyperbola.

Identify the conic by writing the equation in standard form.

Find the vertex and focus of the parabola.

Graph the hyperbola.

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

Find the standard form of the equation of the ellipse with the following characteristics. foci: major axis of length: 12

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 parabola with the given characteristic and vertex at the origin. focus: (0, 7)

Find the vertex and directrix of the parabola.

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

Find the vertices and asymptotes of the hyperbola.

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

Algebraic Expressions and Equations

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Exam 10: Topics in Analytic Geometry

Find the equation of the parabola with vertex at (4, 5) and focus at (-3, 5).

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 1

Find the vertex and directrix of the parabola.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = -3

Find the standard form of the equation of the ellipse with the following characteristics. foci: major axis of length: 20

Find the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (7, 0).

Identify the conic by writing the equation in standard form.

Find the standard form of the equation of the ellipse with the given characteristics. foci: endpoints of the major axis:

Find the center and vertices of the hyperbola.

Identify the conic by writing the equation in standard form.

Find the vertex and focus of the parabola.

Graph the hyperbola.

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

Find the standard form of the equation of the ellipse with the following characteristics. foci: major axis of length: 12

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 parabola with the given characteristic and vertex at the origin. focus: (0, 7)

Find the vertex and directrix of the parabola.

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

Find the vertices and asymptotes of the hyperbola.

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

Algebraic Expressions and Equations

Filters