Question 1

Use the eccentricity of the ellipse to find its equation in standard form. eccentricity   , major axis of length 18 on the x -axis, center at

Accepted Answer

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

Question 2

The antenna of a radio telescope is a paraboloid measuring 66 feet across with a depth of 35 feet. Determine, to the nearest tenth of a foot, the distance from the vertex to the focus of this antenna. Round to the nearest hundredth.

Accepted Answer

A) 2.32 feet 
B) 9.28 feet 
C) 15.56 feet 
D) 31.11 feet 
E) 7.78 feet 
A) 2.32 feet 
B) 9.28 feet 
C) 15.56 feet 
D) 31.11 feet 
E) 7.78 feet

Question 3

Find the equation in standard form of the hyperbola with an asymptote slope of   and foci (2, 1)and (12, 1).

Accepted Answer

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

Question 4

Graph the equation below.

Accepted Answer

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

Question 5

A vertical cross section of a cooling tower is a portion of a hyperbola, as shown in the diagram below. The standard form of the equation of the hyperbolic cross section is   where x and y are measured in feet. The horizontal cross sections of the tower are circles.   What is the smallest radius of a horizontal cross section? Round to the nearest foot.

Accepted Answer

A) 52 feet 
B) 50 feet 
C) 72 feet 
D) 54 feet 
E) 60 feet 
A) 52 feet 
B) 50 feet 
C) 72 feet 
D) 54 feet 
E) 60 feet

Question 6

The line segment that has endpoints on a parabola, passes through the focus of the parabola, and is perpendicular to the axis of symmetry is called the latus rectum of the parabola.   Find the length of the latus rectum for the parabola   .

Accepted Answer

A) 24 
B) 12 
C) 36 
D) 48 
E) 96 
A) 24 
B) 12 
C) 36 
D) 48 
E) 96

Question 7

Use the eccentricity of the ellipse to find its equation in standard form. foci at   , eccentricity

Accepted Answer

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

Question 8

Graph the equation below.

Accepted Answer

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

Question 9

Find the equation in standard form of the hyperbola with asymptotes   and   , and vertices ( 9, 0)and (9, 0).

Accepted Answer

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

Question 10

Identify the graph of the equation below as a parabola, an ellipse, or a hyperbola.

Accepted Answer

A) a parabola 
B) an ellipse 
C) a hyperbola 
A) a parabola 
B) an ellipse 
C) a hyperbola

Question 11

Find the equation in standard form of an ellipse with foci   that passes through the point   .

Accepted Answer

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

Question 12

When a plane exceeds the speed of sound, a sonic boom is produced by the wake of the sound waves. For a plane flying at 13,000 feet, the circular wave front can be given by   where z is the height of the wave front above Earth. See the diagram below. Note that the xy -plane is Earth s surface, which is approximately flat over small distances. Find and name the equation formed when the wave front hits Earth.

Accepted Answer

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

Question 13

Find the acute angle of rotation a that eliminates the xy term. State approximate solution to the nearest 0.1 .

Accepted Answer

A) 75.5 ° 
B) -33.4 ° 
C) 14.5 ° 
D) 22.5 ° 
E) -22.5 ° 
A) 75.5 ° 
B) -33.4 ° 
C) 14.5 ° 
D) 22.5 ° 
E) -22.5 °

Question 14

A line segment with endpoints on the ellipse that is perpendicular to the major axis and passes through a focus is a latus rectum of the ellipse. Find the length of the latus rectum for the ellipse   .

Accepted Answer

A) 40 
B) 2 
C) 5 
D) 1 
E) 10 
A) 40 
B) 2 
C) 5 
D) 1 
E) 10

Question 15

Find the vertices, foci, and asymptotes for the hyperbola given by the equation.

Accepted Answer

A) vertices:   , foci:   , asymptotes:   
B) vertices:   , foci:   , asymptotes:   
C) vertices:   , foci:   , asymptotes:   
D) vertices:   , foci:   , asymptotes:   
E) vertices:   , foci:   , asymptotes:   
A) vertices:   , foci:   , asymptotes:   
B) vertices:   , foci:   , asymptotes:   
C) vertices:   , foci:   , asymptotes:   
D) vertices:   , foci:   , asymptotes:   
E) vertices:   , foci:   , asymptotes:

Question 16

Find the vertex, focus, and directrix of the parabola given by the equation.

Accepted Answer

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

Question 17

Sketch the graph of the polar equation.

Accepted Answer

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

Question 18

Graph the parametric equation by eliminating the parameter.

Accepted Answer

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

Question 19

The parameter t represents time and the parametric equations x = f ( t )and y = g ( t )indicate the x- and y- coordinates of a moving point P as a function of t . Show the motion of the point as t increases by graphing the parametric equations.

Accepted Answer

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

Question 20

Find the equation in standard form of an ellipse with center at (0, 0)minor axis of length 24, and foci at (0, -16)and (0, 16).

Accepted Answer

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

Use the eccentricity of the ellipse to find its equation in standard form. eccentricity , major axis of length 18 on the x -axis, center at

The antenna of a radio telescope is a paraboloid measuring 66 feet across with a depth of 35 feet. Determine, to the nearest tenth of a foot, the distance from the vertex to the focus of this antenna. Round to the nearest hundredth.

Find the equation in standard form of the hyperbola with an asymptote slope of and foci (2, 1)and (12, 1).

Graph the equation below.

The line segment that has endpoints on a parabola, passes through the focus of the parabola, and is perpendicular to the axis of symmetry is called the latus rectum of the parabola. Find the length of the latus rectum for the parabola .

Use the eccentricity of the ellipse to find its equation in standard form. foci at , eccentricity

Graph the equation below.

Find the equation in standard form of the hyperbola with asymptotes and , and vertices ( 9, 0)and (9, 0).

Identify the graph of the equation below as a parabola, an ellipse, or a hyperbola.

Find the equation in standard form of an ellipse with foci that passes through the point .

Find the acute angle of rotation a that eliminates the xy term. State approximate solution to the nearest 0.1 .

A line segment with endpoints on the ellipse that is perpendicular to the major axis and passes through a focus is a latus rectum of the ellipse. Find the length of the latus rectum for the ellipse .

Find the vertices, foci, and asymptotes for the hyperbola given by the equation.

Find the vertex, focus, and directrix of the parabola given by the equation.

Sketch the graph of the polar equation.

Graph the parametric equation by eliminating the parameter.

The parameter t represents time and the parametric equations x = f ( t )and y = g ( t )indicate the x- and y- coordinates of a moving point P as a function of t . Show the motion of the point as t increases by graphing the parametric equations.

Find the equation in standard form of an ellipse with center at (0, 0)minor axis of length 24, and foci at (0, -16)and (0, 16).

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters

Exam 8: Topics in Analytic Geometry

Use the eccentricity of the ellipse to find its equation in standard form. eccentricity , major axis of length 18 on the x -axis, center at

The antenna of a radio telescope is a paraboloid measuring 66 feet across with a depth of 35 feet. Determine, to the nearest tenth of a foot, the distance from the vertex to the focus of this antenna. Round to the nearest hundredth.

Find the equation in standard form of the hyperbola with an asymptote slope of and foci (2, 1)and (12, 1).

Graph the equation below.

The line segment that has endpoints on a parabola, passes through the focus of the parabola, and is perpendicular to the axis of symmetry is called the latus rectum of the parabola. Find the length of the latus rectum for the parabola .

Use the eccentricity of the ellipse to find its equation in standard form. foci at , eccentricity

Graph the equation below.

Find the equation in standard form of the hyperbola with asymptotes and , and vertices ( 9, 0)and (9, 0).

Identify the graph of the equation below as a parabola, an ellipse, or a hyperbola.

Find the equation in standard form of an ellipse with foci that passes through the point .

Find the acute angle of rotation a that eliminates the xy term. State approximate solution to the nearest 0.1 .

A line segment with endpoints on the ellipse that is perpendicular to the major axis and passes through a focus is a latus rectum of the ellipse. Find the length of the latus rectum for the ellipse .

Find the vertices, foci, and asymptotes for the hyperbola given by the equation.

Find the vertex, focus, and directrix of the parabola given by the equation.

Sketch the graph of the polar equation.

Graph the parametric equation by eliminating the parameter.

The parameter t represents time and the parametric equations x = f ( t )and y = g ( t )indicate the x- and y- coordinates of a moving point P as a function of t . Show the motion of the point as t increases by graphing the parametric equations.

Find the equation in standard form of an ellipse with center at (0, 0)minor axis of length 24, and foci at (0, -16)and (0, 16).

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters