JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let the eccentricity of an ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) is reciprocal to that of the hyperbola \(2 x^2-2 y^2=1\). If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is \(................\).
- A \(4\)
- B \(6\)
- C \(2\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(e _{ H }=\sqrt{2}\) \(e _{ E }=\frac{1}{\sqrt{2}}\) Since the curves intersect each other orthogonally The ellipse and the hyperbola are confocal \(H: \frac{x^2}{1 / 2}-\frac{y^2}{1 / 2}=1\) \(\Rightarrow \text { foci }=(1,0)\) For ellipse a.e \(E _{ E }=1\)…
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