Question

Change to polar coordinates the equation: $x^2+y^2=2ax$

Answer 1

General polar form $(r,\theta )$

$r=\sqrt{x^2+y^2}$

$x=r\cos \theta$

$y=r\sin \theta$

$\theta ={\tan }^{-1}\frac{y}{x}$

Now given in the question

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

$\Rightarrow r^2=2a\times r\cos \theta$

$\Rightarrow r=2a\cos \theta$