Question

how do i sketch the curve for (x^2+y^2)^3=4x^2y^2 ?

Answer 1

it is with polar coordinates?

Answer 2

using polar coordinates
@ = theta
x=rcos@
y=rsin@
x^2 + y^2 = r^2
substituting this in
(r^2)^3 = 4(r^2(cos@)^2)(r^2(sin@)^2)
r^6 = 4r^4*(cos@)^2*(sin@)^2
r^2 = 4*(cos@)^2*(sin@)^2
r = 2cos@sin@ = sin(2@)

Answer 3

Alternative curve sketching method, z=given (move 4x... quantity to other side) In the xz, y=0, z=x^6. In yz plane x=0, z=y^6. The shape is like a funky parabola with open bottom.