Question 1

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)    A

Question 2

Find the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (6, 0).

Accepted Answer

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

Question 3

Identify the conic by writing the equation in standard form.

Accepted Answer

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

Question 4

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 5

A solar oven uses a parabolic reflector to focus the sun's rays at a point 8 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 = 8 inches

Accepted Answer

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

Question 6

Find the center and vertices of the ellipse.

Accepted Answer

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

Question 7

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) 28.3 meters 
B) 28.6 meters 
C) 29.1 meters 
D) 30.1 meters 
E) 57.2 meters 
A) 28.3 meters 
B) 28.6 meters 
C) 29.1 meters 
D) 30.1 meters 
E) 57.2 meters

Question 8

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 9

An elliptical stained-glass insert is to be fitted in a   rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.

Accepted Answer

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

Question 10

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -6)

Accepted Answer

A) y2 = -6x 
B) x2 = 6y 
C) x2 = -24y 
D) x2 = -6y 
E) y2 = -24x 
A) y2 = -6x 
B) x2 = 6y 
C) x2 = -24y 
D) x2 = -6y 
E) y2 = -24x

Question 11

Identify the conic by writing the equation in standard form.

Accepted Answer

A)    ; ellipse 
B)    ; circle 
C)    ; circle 
D)    ; ellipse 
E)    ; circle0 
A)    ; ellipse 
B)    ; circle 
C)    ; circle 
D)    ; ellipse 
E)    ; circle0

Question 12

Find the vertex and focus of the parabola.

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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 15

Write the equation of the ellipse that has its center at the origin, focus at (4, 0) and vertex at (7, 0).

Accepted Answer

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

Question 16

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

Question 18

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 19

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 20

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)

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

Find the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (6, 0).

Identify the conic by writing the equation in standard form.

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

A solar oven uses a parabolic reflector to focus the sun's rays at a point 8 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 = 8 inches

Find the center and vertices of the ellipse.

Find the vertices and asymptotes of the hyperbola.

An elliptical stained-glass insert is to be fitted in a rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -6)

Identify the conic by writing the equation in standard form.

Find the vertex and focus of the parabola.

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 parabola and determine the coordinates of the focus.

Write the equation of the ellipse that has its center at the origin, focus at (4, 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 equation of the parabola with vertex at (0, 0) and focus at (0, 4).

Find the center and vertices of the hyperbola.

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

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

Exam 10: Topics in Analytic Geometry

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

Find the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (6, 0).

Identify the conic by writing the equation in standard form.

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

A solar oven uses a parabolic reflector to focus the sun's rays at a point 8 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 = 8 inches

Find the center and vertices of the ellipse.

Find the vertices and asymptotes of the hyperbola.

An elliptical stained-glass insert is to be fitted in a rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -6)

Identify the conic by writing the equation in standard form.

Find the vertex and focus of the parabola.

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 parabola and determine the coordinates of the focus.

Write the equation of the ellipse that has its center at the origin, focus at (4, 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 equation of the parabola with vertex at (0, 0) and focus at (0, 4).

Find the center and vertices of the hyperbola.

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

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