Chapter 10.6, Problem 34AYU

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

$r\left(2-\cos \theta \right)=2$

To determine

To find: Polar equation to a rectangular equation.

Answer to Problem 34AYU

$3x² + 4y² - 4x - 4 = 0$

Explanation of Solution

Given:

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

Formula used:

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

Calculation:

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

$r = \frac{2}{2 - \text{cos}\theta }$

$2r - r\text{cos}\theta = 2$

$2r = 2 + r\text{cos}\theta$

$\left(2r\right)² = \left(2 + x\right)²$

$4x² + 4y² = 4 + x² + 4x$

$3x² + 4y² - 4x - 4 = 0$