How to parameterize this?

(x^2+y^2)^2 = a^2*(x^2-y^2)

So, i need to express that equation in parametric form. What i did was use polar coordinates and i get somethig with the square root of cos 2t, but it doesn't seems convincent to me.

Thanks.

Question

How to parameterize this?

(x^2+y^2)^2 = a^2*(x^2-y^2)

So, i need to express that equation in parametric form. What i did was use polar coordinates and i get somethig with the square root of cos 2t, but it doesn't seems convincent to me.

Thanks.

anonymous · Answer

Take the equations which relate x and y coordinates to r and θ and simply substitute them into the above equation and simplify.

anonymous · Answer

Why doesn't the answer you got convince you?

anonymous · Answer

I've plotted the  equation and i get one of the so called "Lissajous Curves". And those curves , in parametric form don't envolve square roots of cosines of double angles.
So i think i'm making some mistake.