Question 1

Find a polar equation in r and   of the parabola with focus at the pole and the given vertex.

Accepted Answer

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

Question 2

Find an equation of the parabola that satisfies the condition. Focus   , directrix

Accepted Answer

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

Question 3

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Accepted Answer

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

Question 4

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Accepted Answer

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B)    
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D)    
E)    
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E)

Question 5

Find a parametrization that gives the same graph as the given equation.

Accepted Answer

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E)

Question 6

Sketch the graph of the polar equation

Accepted Answer

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D)    
A)    
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D)

Question 7

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Accepted Answer

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B)    
C)    
D)    
E)    
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E)

Question 8

Change the rectangular coordinates   to polar coordinates with   and   .

Accepted Answer

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E)

Question 9

Find an equation for the parabola shown in the figure.

Accepted Answer

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Question 10

Find an equation of the parabola that satisfies the condition. Vertex   , focus

Accepted Answer

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E)

Question 11

Polar equations of conics can be used to describe the motion of comets. These paths can be graphed using the following polar equation, where e is the eccentricity of the conic and r per  is the perihelion distance measured in AU. For Encke's Comet r per  = 0.3317 and e = 0.8499, determine whether its trajectory is elliptical, parabolic, or hyperbolic.

Accepted Answer

A) parabolic 
B) elliptical 
C) hyperbolic 
A) parabolic 
B) elliptical 
C) hyperbolic

Question 12

Change the rectangular coordinates   to polar coordinates with   and   .

Accepted Answer

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

Question 13

Polar equations of conics can be used to describe the motion of comets. These paths can be graphed using the following polar equation, where e is the eccentricity of the conic and r per  is the perihelion distance measured in AU. For Comet 1973.99 r per  = 0.142 and e = 1.000, determine whether its trajectory is elliptical, parabolic, or hyperbolic.

Accepted Answer

A) elliptical 
B) hyperbolic 
C) parabolic 
A) elliptical 
B) hyperbolic 
C) parabolic

Question 14

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Accepted Answer

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

Question 15

Find an equation for the ellipse that has its center at the origin and satisfies the conditions.

Accepted Answer

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

Question 16

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Accepted Answer

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

Question 17

Polar equations of conics can be used to describe the motion of comets. These paths can be graphed using the following polar equation, where e is the eccentricity of the conic and r per  is the perihelion distance measured in AU. The orbit of Saturn has r per  = 9.006 and e = 0.056. The motion of Comet 1973.99 has r per  = 0.142 and e = 2.718282. Graph both the motion of the comet and the orbit of Saturn.

Accepted Answer

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

Question 18

Find an equation of the parabola that satisfies the condition. Vertex   , focus

Accepted Answer

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

Question 19

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C, and indicate the orientation.   t in

Accepted Answer

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B)    
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A)    
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D)    
E)

Question 20

Find an equation for the set of points in an xy-plane such that the sum of the distances from   and   is   .

Accepted Answer

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B)    
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E)

Find a polar equation in r and of the parabola with focus at the pole and the given vertex.

Find an equation of the parabola that satisfies the condition. Focus , directrix

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Find a parametrization that gives the same graph as the given equation.

Sketch the graph of the polar equation

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Change the rectangular coordinates to polar coordinates with and .

Find an equation for the parabola shown in the figure.

Find an equation of the parabola that satisfies the condition. Vertex , focus

Change the rectangular coordinates to polar coordinates with and .

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Find an equation for the ellipse that has its center at the origin and satisfies the conditions.

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Find an equation of the parabola that satisfies the condition. Vertex , focus

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C, and indicate the orientation. t in

Find an equation for the set of points in an xy-plane such that the sum of the distances from and is .

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

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Exam 11: Topics From Analytic Geometry

Find a polar equation in r and of the parabola with focus at the pole and the given vertex.

Find an equation of the parabola that satisfies the condition. Focus , directrix

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Find a parametrization that gives the same graph as the given equation.

Sketch the graph of the polar equation

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Change the rectangular coordinates to polar coordinates with and .

Find an equation for the parabola shown in the figure.

Find an equation of the parabola that satisfies the condition. Vertex , focus

Change the rectangular coordinates to polar coordinates with and .

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Find an equation for the ellipse that has its center at the origin and satisfies the conditions.

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola.

Find an equation of the parabola that satisfies the condition. Vertex , focus

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C, and indicate the orientation. t in

Find an equation for the set of points in an xy-plane such that the sum of the distances from and is .

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Filters