Question

Convert x2 + y2 -4x = 0 to polar form.

Answer 1

`r(r-4\cos \theta)=0`

Explanation:

We are given the following equation:

`x^2 + y^2 -4x = 0`

We have to convert it into polar form.

We put

`x = r \cos \theta\\y = r\sin \theta`

Putting values, we get:

`x^2 + y^2 -4x = 0\\(r\cos \theta)^2 + (r\sin \theta)^2 - 4(r\cos \theta) = 0\\r^2(\cos^2 \theta + \sin^2 \theta) - 4r\cos \theta = 0\\r^2 - 4r\cos \theta = 0\\r(r-4\cos \theta)=0`

is the required polar form.