   Chapter 12.6, Problem 8E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS3-10 Finding a Polar Equation for a Conic Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions.Ellipse, eccentricity 0.6 , directrix r = 2 csc θ

To determine

The polar equation of an ellipse.

Explanation

Given:

The eccentricity and directrix of the ellipse is as follows.

e=0.6r=2cscθ

Approach:

Convert the equation in Cartesian equation.

r=2sinθrsinθ=2y=2

Since the directrix is y=2, it is to the above to the focus. Thus the polar equation of ellipse is r=ed1+esinθ(1)

Calculation:

Here, 0<e<1

Substituting 0.6 for e and 2 for d in equation (1),

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