A circle $C_{1}$ passes through the origin $O$ and has diameter $4$ on the positive $x$-axis. The line $y =2 x$ gives a chord $OA$ of a circle $C _{1}$. Let $C _{2}$ be the circle with $OA$ as a diameter. If the tangent to $C _{2}$ at the point $A$ meets the $x$-axis at $P$ and $y$-axis at $Q$, then $QA : AP$ is equal to.
A circle $C_{1}$ passes through the origin $O$ and has diameter $4$ on the positive $x$-axis. The line $y =2 x$ gives a chord $OA$ of a circle $C _{1}$. Let $C _{2}$ be the circle with $OA$ as a diameter. If the tangent to $C _{2}$ at the point $A$ meets the $x$-axis at $P$ and $y$-axis at $Q$, then $QA : AP$ is equal to.
- [JEE MAIN 2022]
- A
$1:4$
- B
$1: 5$
- C
$2: 5$
- D
$1: 3$
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