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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

29-30 Identifying and Graphing a Conic (a) Find the eccentricity, and identify the conic. (b) Sketch the conic, and label the vertices.

3 1. r = 2 1 cos θ

To determine

a)

To find:

The eccentricity, and identify the conic.

Explanation

Given:

The conic is given as,

r=21cosθ

Approach:

The two formulas r=ed1±ecosθ or r=ed1±esinθ represent conics with eccentricity e.

We compare the given equation of conic with these standard equations to find the eccentricity.

Then,

e<1 for an ellipse

e=1 for a parabola

e>1 for a hyperbola

To determine

b)

To sketch:

The conic, and label the vertices.

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