JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
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 \(1:4\)
- B \(1: 5\)
- C \(2: 5\)
- D \(1: 3\)
Answer & Solution
Correct Answer
(A) \(1:4\)
Step-by-step Solution
Detailed explanation
\(C _{2}\) is a circle with \(OA\) as diameter. So, tangent at \(A\) on \(C _{2}\) is perpendicular to \(OR\) Let \(OA =\ell\) \(\therefore \frac{ QA }{ AP }=\frac{\ell \cot \theta}{\ell \tan \theta}\) \(=\frac{1}{\tan ^{2} \theta}=\frac{1}{4}\)
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