Chapter 10.6, Problem 25AYU

In Problems 25-36, convert each polar equation to a rectangular equation.

$r=\frac{1}{1+\cos \theta }$

To determine

To find: Polar equation to a rectangular equation.

Answer to Problem 25AYU

$y²+2x-1=0$

Explanation of Solution

Given:

$r=\frac{1}{1+\text{ cos}\theta }$

Formula used:

$x=r\text{cos}\theta ,y=r\text{sin}\theta$; $r²=x²+y²$

Calculation:

Given $r=\frac{1}{1+\text{ cos}\theta }$

$r+r\text{cos}\theta =1$

$r=1-r\text{cos}\theta$

$r²=\left(1-r\text{cos}\theta \right)²$

$r²=\left(1-x\right)²$

$x²+y²=1+x²-2x$

$y²+2x-1=0$