JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Consider a hyperbola \(H : x ^{2}-2 y ^{2}=4\). Let the tangent at a point \(P (4, \sqrt{6})\) meet the \(x\) -axis at \(Q\) and latus rectum at \(R \left( x _{1}, y _{1}\right), x _{1}>0 .\) If \(F\) is a focus of \(H\) which is nearer to the point \(P\), then the area of \(\Delta QFR\) is equal to ....... .
- A \(4 \sqrt{6}\)
- B \(\sqrt{6}-1\)
- C \(\frac{7}{\sqrt{6}}-2\)
- D \(4 \sqrt{6}-1\)
Answer & Solution
Correct Answer
(C) \(\frac{7}{\sqrt{6}}-2\)
Step-by-step Solution
Detailed explanation
\(\frac{x^{2}}{4}-\frac{y^{2}}{2}=1\) \(e=\sqrt{1+\frac{b^{2}}{a^{2}}}=\sqrt{\frac{3}{2}}\) \(\therefore\) Focus \(F ( ae , 0) \Rightarrow F (\sqrt{6}, 0)\) equation of tangent at \(P\) to the hyperbola is \(2 x-y \sqrt{6}=2\) tangent meet \(x\) -axis at \(Q(1,0)\) And latus…
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