Let $x=\frac{a(ac\sin^{2}\alpha+b^{2}\cos \alpha)}{a^{2}\sin^{2}\alpha+b^{2}\cos^{2}\alpha}$ and $y=,\frac{ab\sin \alpha(a-c\cos \alpha)}{a^{2}\sin^{2}\alpha+b^{2}\cos^{2}\alpha}$.

Prove: $x^2+y^2=1$

Could you please help me to prove this? I only get extremely long terms if I try to square $x$ and $y$. $sin^2+cos^2=1$ doesn't seem to help either.