Question

How do you convert `2y= -3x^2+3x` into a polar equation?

Answer 1

`3r=3sectheta-2tanthetasectheta`

Explanation:

To convert the equation `2y=−3x^2+3x` into a polar equation, we should use `y=rcostheta` and `x=rsintheta`.

Putting these, the equation becomes

`2rsintheta=-3r^2cos^2theta+3rcostheta` dividing by `r` and transposing

or `3rcos^2theta=3costheta-2sintheta`

or `3r=3sectheta-2tanthetasectheta`