How can I solve this form of quadratic? It has no $\sin(t)\cos(t)$ term.
$$(\cos(t) + p + a)^2 - a^2 + b (\sin(t) + q)^2 = 0$$
$$\cos^2(t) + 2(a+p)\cos(t) + b\sin^2(t) + 2bq\sin(t) + (p^2 + 2ap + bq^2) = 0$$
I'm at a loss for anything short of writing it out in complex exponentials. Is there another technique?