JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Points \(P (-3,2), Q (9,10)\) and \(R (\alpha, 4)\) lie on a circle \(C\) with \(P R\) as its diameter. The tangents to \(C\) at the points \(Q\) and \(R\) intersect at the point \(S\). If \(S\) lies on the line \(2 x - ky =1\), then \(k\) is equal to \(.........\).
- A \(3\)
- B \(6\)
- C \(9\)
- D \(12\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
\(m _{ PQ } \cdot m _{ QR }=-1\) \(\Rightarrow \frac{10-2}{9+3} \times \frac{10-4}{9-\alpha}=-1 \Rightarrow \alpha=13\) \(m _{ op } \cdot m _{ Qs }=-1 \Rightarrow m _{ Qs }=-\frac{4}{7}\) Equation of \(QS\) \(y-10=-\frac{4}{7}(x-9)\) \(\Rightarrow 4 x+7 y=106 \ldots(1)\)…
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