Question

how do I convert r^2=2sin2theta to Cartesian form

Answer 1

r^2 = 2sin(2theta)
r^2 = 2 * 2sin(theta) cos(theta)

r^2 = x^2 + y^2
cos(theta) = x/r
sin(theta) = y/r

(x^2+y^2)^2 = 4 (y/r) (x/r)

(x^2 + y^2)^2 = 4xy / r^2

r^2 (x^2 + y^2)^2 = 4xy

(x^2 + y^2)^2 (x^2 + y^2)^2 = 4xy

(x^2 + y^2)^2

Answer 2

(x^2 + y^2)^4 = 4xy