JEE Math Practice Question

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 :

1. A.1 : 4
2. B.1 : 5
3. C.2 : 5
4. D.1 : 3