   Chapter 12.CT, Problem 17CT ### 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

# (a) Find the polar equation of the conic that has a focus at the origin, eccentricity e = 1 2 , and directive x = 2 . Sketch a graph of the conic.(b) What type of conic is represented by the following equation? Sketch its graph. r = 3 2 − sin θ

To determine

(a)

To find:

The polar equation of the conic and sketch a graph of the conic.

Explanation

Given:

The polar equation of the conic that has a focus at the origin, eccentricity e=12, and directive x=2.

Approach:

The general equation of a conic with eccentricity e and directrix x=d is,

r=ed1+ecosθ(1)

Calculation:

From the given information, e=12 and d=2.

Substitute 12 for e, 2 for d in equation (1).

To determine

(b)

To find:

The type of conic and sketch the graph.

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