JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(P \left(\frac{2 \sqrt{3}}{\sqrt{7}}, \frac{6}{\sqrt{7}}\right), Q , R\) and \(S\) be four points on the ellipse \(9 x^2+4 y^2=36\). Let \(P Q\) and \(RS\) be mutually perpendicular and pass through the origin. If \(\frac{1}{( PQ )^2}+\frac{1}{( RS )^2}=\frac{ p }{ q }\), where \(p\) and \(q\) are coprime, then \(p+q\) is equal to \(.........\).
- A \(143\)
- B \(137\)
- C \(157\)
- D \(147\)
Answer & Solution
Correct Answer
(C) \(157\)
Step-by-step Solution
Detailed explanation
Let \(R (2 \cos \theta, 3 \sin \theta)\) as \(OP \perp OR\) \(\text { so } \frac{3 \sin \theta}{2 \cos \theta} \times \frac{\frac{6}{\sqrt{7}}}{\frac{2 \sqrt{3}}{\sqrt{7}}}=-1\) \(\Rightarrow \tan \theta=\frac{-2}{3 \sqrt{3}}\)…
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