Question

How to convert `r=8+3costheta` to rectangular form?

Sorry, another of these questions. I can't figure out what I'm supposed to do with it so any help is appreciated.

Answer 1

`(x^4+2x^2y^2-6x^3+y^4-6y^2x-55x^2)/64= y^2`

Explanation:

`r=8+3costheta`

`r^2=8r+3rcostheta`

`x^2+y^2= 8r+3x`

`(x^2+y^2-3x)^2= (8r)^2`

`x^4+2x^2y^2-6x^3+y^4-6y^2x+9x^2= 64(x^2+y^2)`

`(x^4+2x^2y^2-6x^3+y^4-6y^2x-55x^2)/64= y^2`

This one works and gives me a limacon
graph{ (x^4+2x^2y^2-6x^3+y^4-6y^2x-55x^2)/64= y^2 [-15.31, 22.65, -9.6, 9.38]}