Question 1

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

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Question 2

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

Question 3

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 4

Sketch the graph of the polar equation.

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Question 5

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

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Question 6

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 7

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

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Question 8

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

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Question 9

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 10

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

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 polar equation.

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

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 ellipse that has its center at the origin and satisfies the conditions.

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

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.

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

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 polar equation.

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

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 ellipse that has its center at the origin and satisfies the conditions.

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

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.

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