Question 1

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

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Question 2

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

Question 3

Find the foci of the ellipse.

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Question 4

Shown in the figure is the Lissajous figure given by   Find the period of the figure - that is, the length of the smallest t-interval that traces the curve.

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Question 5

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

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Question 6

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.

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Question 7

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

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Question 8

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)    
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Question 9

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

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Question 10

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

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. 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.

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Question 12

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

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Question 13

The parametric equations specify the position of a moving point P ( x, y ) at time t. Sketch the graph.

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Question 14

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

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Question 15

Change the rectangular coordinates   to polar coordinates with   and   .

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Question 16

Sketch the graph of the polar equation.

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Question 17

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

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Question 18

Find an equation for the indicated half of the parabola.

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Question 19

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

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Question 20

The parametric equations specify the position of a moving point P ( x, y ) at time t. Sketch the graph.

Accepted Answer

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B)    
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D)    
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B)    
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D)

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

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 the foci of the ellipse.

Shown in the figure is the Lissajous figure given by Find the period of the figure - that is, the length of the smallest t-interval that traces the curve.

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

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.

Find an equation of the parabola that satisfies the condition. Vertex , 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 for the ellipse that has its center at the origin and satisfies the conditions.

The parametric equations specify the position of a moving point P ( x, y ) at time t. Sketch the graph.

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

Change the rectangular coordinates to polar coordinates with and .

Sketch the graph of the polar equation.

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

Find an equation for the indicated half of the parabola.

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

The parametric equations specify the position of a moving point P ( x, y ) at time t. Sketch the graph.

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 that has the same graph as the equation in x and y.

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 the foci of the ellipse.

Shown in the figure is the Lissajous figure given by Find the period of the figure - that is, the length of the smallest t-interval that traces the curve.

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

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.

Find an equation of the parabola that satisfies the condition. Vertex , 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 for the ellipse that has its center at the origin and satisfies the conditions.

The parametric equations specify the position of a moving point P ( x, y ) at time t. Sketch the graph.

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

Change the rectangular coordinates to polar coordinates with and .

Sketch the graph of the polar equation.

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

Find an equation for the indicated half of the parabola.

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

The parametric equations specify the position of a moving point P ( x, y ) at time t. Sketch the graph.

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