JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(\mathrm{P}\) be a point on the hyperbola \(\mathrm{H}: \frac{\mathrm{x}^2}{9}-\frac{\mathrm{y}^2}{4}=1\), in the first quadrant such that the area of triangle formed by \(\mathrm{P}\) and the two foci of \(\mathrm{H}\) is \(2 \sqrt{13}\). Then, the square of the distance of \(\mathrm{P}\) from the origin is
- A \(18\)
- B \(26\)
- C \(22\)
- D \(20\)
Answer & Solution
Correct Answer
(C) \(22\)
Step-by-step Solution
Detailed explanation
\(\frac{\mathrm{x}^2}{9}-\frac{\mathrm{y}^2}{4}=1\) \(\mathrm{a}^2=9, \mathrm{~b}^2=4\) \(\mathrm{~b}^2=\mathrm{a}^2\left(\mathrm{e}^2-1\right) \Rightarrow \mathrm{e}^2=1+\frac{\mathrm{b}^2}{\mathrm{a}^2}\) \(\mathrm{e}^2=1+\frac{4}{9}=\frac{13}{9} \)…
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