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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

77-80 Polar Equation of Conics A polar equation of a conic is given.(a) Find the eccentricity, and identify the conic.(b) Sketch the conic, and label the vertices.

r = 4 1 + 2 sin θ

To determine

(a)

To find:

The eccentricity, and identify the conic.

Explanation

Given:

r=41+2sinθ

Approach:

A polar equation of the form r=ed1±ecosθ or r=ed1±esinθ represents a conic with one focus at the origin and with eccentricity e. The conic is

a parabola if e=1(1)

an ellipse if 0

To determine

(b)

To sketch:

The conic and label the vertices.

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