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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Identifying and Sketching a Conic In Exercises 113-118, find the eccentricity and the distance from the pole to the directrix of the conic. Then identify the conic and sketch its graph. Use a graphing utility to confirm y our results.

r = 6 1 + sin θ

To determine

To calculate: The eccentricity of graph of the polar equation r=61sinθ and the distance between the pole to the directrix of the conic. Then, identify the type of conic and sketch its graph with the help of graphing utility to verify your results.

Explanation

Given:

The provided polar equation is r=61sinθ.

Formula used:

The standard equation of a conic with eccentricity e and distance between the pole to the directrix d is:

r=ed1esinθ

Calculation:

The provided polar equation is;

r=61sinθ

The standard equation of a conic with eccentricity e and distance between the pole to the directrix d is:

r=ed1esinθ

Compare the provided equation with the standard equation r=ed1esinθ,

ed=6

So, eccentricity is;

e=1

The distance between the pole to the directrix of the conic is;

d=6

Since, when eccentricity is 1 the conic is a parabola

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