Question

Transform the equation $r=6\cos \left(\theta \right)$from polar coordinate to rectangular coordinate.

Short answer

The rectangular equation is

$x^2+y^2=6x$

Step-by-step solution

Step 1. Given information

Polar equation is

$r=6\cos \left(\theta \right)$

Step 2. Change the equation into rectangular form

The polar equation is

$r=6\cos \left(\theta \right)$

Multiply both sides by r

$$\begin{gathered} r\times r=r\times 6\cos \left(\theta \right) \\ {r}^2=6r\cos \left(\theta \right) \end{gathered}$$

Apply conversion formula

$$\begin{gathered} r^2=x^2+y^2 \\ x=r\cos \left(\theta \right) \end{gathered}$$

Plug these values into the polar equation

So, the polar equation is

$x^2+y^2=6x$