Question

How do you find the rectangular equation for `r=2+2costheta`?

Answer 1

`x^2 + y^2 - 2x - 2sqrt(x^2 + y^2) = 0`

Explanation:

Multiply both sides by r:

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

Substitute `sqrt(x^2 + y^2)` for `r`, `x^2 + y^2` for `r^2` and `x` for `rcos(theta)`

`x^2 + y^2 = 2sqrt(x^2 + y^2) + 2x`

Move everything to the left:

`x^2 + y^2 - 2x - 2sqrt(x^2 + y^2) = 0`