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  4. A circle C1 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 :

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Q. 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 :

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Solution:

$ C_1: x^2+y^2-4 x=0$
$ \tan \theta=2$
image
$C _2$ is a circle with $OA$ as diameter.
So, tangent at $A$ on $C _2$ is perpendicular to $OR$
image