Question 1

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

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Question 2

Lissajous figures are used in the study of electrical circuits to determine the phase difference   between a known voltage   and an unknown voltage   having the same frequency. The voltages are graphed parametrically as   and   . If   is acute, then   where y int  is the nonnegative y -intercept and y max  is the maximum y-value on the curve. Graph the parametric curve and use the graph to approximate   in degrees if

Accepted Answer

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Question 3

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

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Question 4

Find an equation for the indicated half of the parabola.

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Question 5

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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Question 6

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C.   -1   t   1

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Question 7

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

Accepted Answer

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Question 8

An arch of a bridge is semi-elliptical, with major axis horizontal. The base of the arch is 30 feet across, and the highest part of the arch is 10 feet above the horizontal roadway, as shown in the figure. Find the height of the arch 7 feet from the center of the base.

Accepted Answer

A) 11.0 ft 
B) 17.7 ft 
C) 8.8 ft 
D) 12.1 ft 
E) 7.3 ft 
A) 11.0 ft 
B) 17.7 ft 
C) 8.8 ft 
D) 12.1 ft 
E) 7.3 ft

Question 9

Find an equation in x and y for the polar equation.

Accepted Answer

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Question 10

Find an equation for the set of points in an xy-plane such that the difference of the distances from F and F ' is k.

Accepted Answer

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Question 11

Find a polar equation in r and   that has the same graph as the equation in x and y.

Accepted Answer

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E)

Question 12

Classify the conic.

Accepted Answer

A) parabola 
B) ellipse 
C) circle 
D) hyperbola 
A) parabola 
B) ellipse 
C) circle 
D) hyperbola

Question 13

Find an equation for the ellipse shown in the figure.

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Question 14

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C.   -1   t   1

Accepted Answer

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

Question 15

Find a polar equation in r and   that has the same graph as the equation in x and y.

Accepted Answer

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

Question 16

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

Accepted Answer

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

Question 17

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

Accepted Answer

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

Question 18

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

Accepted Answer

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

Question 19

Sketch the graph of the ellipse, showing the foci .

Accepted Answer

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D)    
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B)    
C)    
D)

Question 20

Find a polar equation in r and   that has the same graph as the equation in x and y.

Accepted Answer

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

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

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

Find an equation for the indicated half of the parabola.

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 in x and y whose graph contains the points on the curve C. Sketch the graph of C. -1 t 1

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

An arch of a bridge is semi-elliptical, with major axis horizontal. The base of the arch is 30 feet across, and the highest part of the arch is 10 feet above the horizontal roadway, as shown in the figure. Find the height of the arch 7 feet from the center of the base.

Find an equation in x and y for the polar equation.

Find an equation for the set of points in an xy-plane such that the difference of the distances from F and F ' is k.

Find a polar equation in r and that has the same graph as the equation in x and y.

Classify the conic.

Find an equation for the ellipse shown in the figure.

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C. -1 t 1

Find a polar equation in r and that has the same graph as the equation in x and y.

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

Sketch the graph of the ellipse, showing the foci .

Find a polar equation in r and that has the same graph as the equation in x and y.

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 an equation of the parabola that satisfies the condition. Vertex , directrix

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

Find an equation for the indicated half of the parabola.

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 in x and y whose graph contains the points on the curve C. Sketch the graph of C. -1 t 1

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

An arch of a bridge is semi-elliptical, with major axis horizontal. The base of the arch is 30 feet across, and the highest part of the arch is 10 feet above the horizontal roadway, as shown in the figure. Find the height of the arch 7 feet from the center of the base.

Find an equation in x and y for the polar equation.

Find an equation for the set of points in an xy-plane such that the difference of the distances from F and F ' is k.

Find a polar equation in r and that has the same graph as the equation in x and y.

Classify the conic.

Find an equation for the ellipse shown in the figure.

Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C. -1 t 1

Find a polar equation in r and that has the same graph as the equation in x and y.

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix.

Sketch the graph of the ellipse, showing the foci .

Find a polar equation in r and that has the same graph as the equation in x and y.

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