   Chapter 10.6, Problem 24E

Chapter
Section
Textbook Problem

Identifying a Conic In Exercises 23-26, use a graphing utility to graph the polar equation. Identify the graph and find its eccentricity. r = − 15 2 + 8 sin θ

To determine

To Calculate:

The sketch of the polar equation r=152+8sinθ using graphing utility and identify the graph and also find its eccentricity.

Explanation

Given: The provided polar equation is r=152+8sinθ

Formula Used:

For the equation of the type r=ed1+esinθ, e is the eccentricity and d is the distance between focus at pole and corresponding directrix.

Calculation:

Consider the polar equation of the conic as: r=ed1+esinθ

Here e is eccentricity and d is distance between focus at pole and corresponding directrix.

The equation can be re-written as,

r=152(1+4sinθ)

r=152(1+4sinθ)

Compare it with the standard equation to get,

e=4

Hence, for e>1, the conic is a hyperbola

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