Question

How do you convert `(x^2 + y^2)^(3/2) = 3y^2 - 3x^2` to polar form?

Answer 1

`r^3= 3 cos 2theta`

Explanation:

In polar form x equals `r cos theta` and y equals `rsin theta`. Accordingly, `x^2+y^2= r^2` and `y^2-x^2= cos^2 theta -sin^2 theta = cos 2theta`

The given expression in polar form would thus be `r^3= 3 cos 2theta`