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Chapter 10: Q 5. (page 683)

True or False:If (r,胃)are polar coordinates, the equation r=22+3sin(胃)defines a hyperbola.

Short Answer

Expert verified

This statement is True.

Step by step solution

01

Step 1. Given information

The polar equation is

r=22+3sin(胃)

02

Step 2. Checking the statement

The polar equation is

r=22+3sin(胃)

Divide top and bottom by 2

r=2222+32sin(胃)r=11+32sin(胃)

Compare with the standard polar equation

r=ep1+esin(胃)

So,

e=32>1

Therefore, this polar equation is a hyperbola.

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