   Chapter 10.6, Problem 10E

Chapter
Section
Textbook Problem

# (a) Find the eccentricity, (b) identify the conic, (c) give an equation of the directrix, and (d) sketch the conic.10. r = 1 2 + sin θ

(a)

To determine

To find: The eccentricity for the given equation.

Explanation

Given:

The given polar equation is r=12+sinθ.

Calculation:

Calculate the eccentricity for the given equation.

The polar equation for the given equation will be either r=ed1±esinθ

Make the given equation to polar equation, divide the given equation by 2.

r=12+sinθ=(12)(22+12sinθ

(b)

To determine

To identify: The shape of conic.

(c)

To determine

To find: The equation of directrix.

(d)

To determine

To draw: The shape of a conic.

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