Question

Convert the polar equation r = 2 cos to a Cartesian equation.x + y = 2xx^2 + y^2 = 2yx^2 + y^2 = 2x

Answer 1

Step 1

Given r = 2cosθ

Draw the diagram

From the diagram,

$\begin{gathered} y=\text{ rsin}\theta \\ x=r\cos \theta \\ \text{But given r = 2cos}\theta \\ r^2=2rcos\theta \end{gathered}$$\begin{gathered} r^2=\text{ 2}\times r\cos \theta=\text{ 2x} \\ \text{But} \\ x^2+y^2=r^2 \end{gathered}$

Hence

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