Question

convert polar equation to rectangular coordinates:

r^2=4sin2(theta)

Answer 1

conversion formulas
r^2 = x^2 + y^2
sinØ = y/r
cosØ = x/r

r^2 = 4 sin 2Ø
r^2 = 4(2sinØcosØ) = 8sinØcosØ
x^2 + y^2 = 8(y/r)(x/r)
= 8xy/r^2
x^2 + y^2 = 8xy/(x^2 + y^2)
(x^2 + y^2)^2 = 8xy