Circle

A circle $C_{1}$ passes through the origin $\mathrm{O}$ and has diameter 4 on the positive $x$-axis. The line $y=2 x$ gives a chord $\mathrm{OA}$ of circle $\mathrm{C}_{1}$. Let $\mathrm{C}_{2}$ be the circle with $\mathrm{OA}$ as a diameter. If the tangent to $\mathrm{C}_{2}$ at the point $\mathrm{A}$ meets the $x$-axis at $\mathrm{P}$ and $y$-axis at $\mathrm{Q}$, then $\mathrm{QA}: \mathrm{AP}$ is equal to :