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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

8. (a) Write polar equations that represent a conic with eccentricity e . For what values of e is the conic an ellipse? a hyperbola? a parabola?

(b) What conic does the polar equation r = 2 / 1 cos θ represent? Graph the conic.

To determine

a)

The polar equations that represent a conic with eccentricity e and values of e for which conic is an ellipse, a hyperbola, and a parabola.

Explanation

Approach:

The polar equation of the conic has the form,

r=ed1±ecosθ

Or,

r=ed1±esinθ

Here, e is the eccentricity and d is the distance from the directrix of conic.

The above equations represent an ellipse if eccentricity e is equals to 1. It represents a hyperbola if 0<e<1 and a parabola if eccentricity e is greater than 1

To determine

(b)

To find:

The conic that the polar equation r=2(1cosθ) represents and graph of the conic.

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Chapter 12 Solutions

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