Question

What the is the polar form of `sqrt(x^2+y^2) = 6x+7y-x^2y-2xy`?

Answer 1

We know the relations

`x=rcostheta and y =rsintheta`

Again `x^2+y^2=r^2`

where r and `theta` are the polar coordinate of a point having rectangular coordinate `(x,y)`

The given equation in rectanglar form is

`sqrt(x^2+y^2)=6x+7y-x^2y-2xy`

`=>sqrt(r^2)=6rcostheta+7rsintheta-r^3cos^2thetasintheta-2r^2costhetasintheta`

`=>r=6rcostheta+7rsintheta-r^3cos^2thetasintheta-r^2sin2theta`

`=>6costheta+7sintheta-r^2cos^2thetasintheta-rsin2theta=1`

This is the polar form of the given equation.