   Chapter 10.6, Problem 9E

Chapter
Section
Textbook Problem

# Matching In Exercises 7-12, match the polar equation with its correct graph. [The graphs are labeled (a), (b), (c), (d>, (e), and (f).]  r = 3 1 − 2 sin θ

To determine

The correct match of the given polar equation with its correct graph from the options given.

Explanation

Given: Given options for graphs are labelled as (a), (b), (c), (d), (e) and (f)as shown below.

Calculation: The given equation is r=312sinθ.

Since e=2>1, the graph of the given equation is a hyperbola.

Because d=32, the directrix is the line y=32 and the transverse axis of the hyperbola lies on the line θ=π2. Also, vertices are at (3,π2) and (1,3π2)

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