Question

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

Answer 1

`r^2(3cos^2theta+3sinthetacostheta-2sin^2theta)=3`

Explanation:

The relation between polar coordinates `(r,theta)` and Cartesian coordinates `(x,y)` is given by `x=rcostheta`, `y=rsintheta` and `x^2+y^2=r^2`

Hence `3=3x^2+3xy-2y^2`

`hArr3r^2cos^2theta+3r^2sinthetacostheta-2r^2sin^2theta=3`

or `r^2(3cos^2theta+3sinthetacostheta-2sin^2theta)=3`