Question

How do you write the polar equations for `y^2=2x`?

Answer 1

`r^2 sin^2(theta) = 2rcos(theta)`

Explanation:

In polar coordinates, the coordinates are

`x=rcos(theta)`
`y=rsin(theta)`

So,

`y^2=2x \to r^2 sin^2(theta) = 2rcos(theta)`

If `r \ne 0` (which means `(x,y)\ne (0,0)`, we can simplify one `r` and have

`rsin^2(theta)=2cos(theta)`