Question

How do you convert `x^2+y^2 = 2x^2` to polar form?

Answer 1

`theta = 45º` or `theta = –45º`

Explanation:

First, simplify the expression:

`x^2 + y^2 = 2x^2`
`y^2 = x^2`

Using the parameterisation `x = r cos theta` and `y = r sin theta`, make the appropriate substitutions:

`r^2 cos^2 theta = r^2 sin^2 theta`
`tan^2 theta = 1`
`tan theta = pm 1`
`theta = 45º` or `theta = –45º`

`r` in this case is any positive real value.