Chapter 10, Problem 30RE

To determine

To find: The rectangular equation for the polar equation given.

Answer to Problem 30RE

$y²-8x-16=0$

Explanation of Solution

Given:

$r=\frac{4}{1-\text{ cos}\theta }$

Formula Used:

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

Calculation:

$r=\frac{4}{1-\text{ cos}\theta }$

$r\left(1-\text{ cos}\theta \right)=4$

$r-r\text{cos }=4$

$r=4+r\text{cos}\theta$

$x²+y²={\left(4+x\right)}^2$

$x^2+y^2=x^2+8x+16$

$y²-8x-16=0$