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Chapter 10: Q 10. (page 683)

Identify the conic that each polar equation represents. Also, give the position of the directrix.

r=21+2cos(胃)

Short Answer

Expert verified

This polar equation is a hyperbola.

The equation of directrix isx=1

Step by step solution

01

Step 1. Given information

The polar equation is

r=21+2cos(胃)

02

Step 2. Finding e and p

The polar equation is

r=21+2cos(胃)

Compare with the standard polar equation

r=ep1+ecos(胃)

So,

ep=2e=22脳p=2p=1

03

Step 3. Identify the conic equation

We have got

e=2>1

So, this is a hyperbola equation.

04

Step 4. Finding the directrix equation

The formula for the directrix equation is

x=p

Plug values p=1

So, the directrix equation isx=1

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