JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
An ellipse passes through the foci of the hyperbola, \(9x^2 - 4y^2 = 36\) and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is \(\frac {1}{2}\), then which of the following points does not lie on the ellipse?
- A \(\left( {\sqrt {\frac{{13}}{2}} ,\sqrt 6 } \right)\)
- B \(\left( {\frac{{\sqrt {39} }}{2},\sqrt 3 } \right)\)
- C \(\left( {\frac{1}{2}\sqrt {13} ,\frac{{\sqrt 3 }}{2}} \right)\)
- D \((\sqrt {13} ,0)\)
Answer & Solution
Correct Answer
(C) \(\left( {\frac{1}{2}\sqrt {13} ,\frac{{\sqrt 3 }}{2}} \right)\)
Step-by-step Solution
Detailed explanation
Equation of hyperbola is \(\frac{{{x^2}}}{4} - \frac{{{y^2}}}{9} = 1\) Its foci \( = \left( { \pm \sqrt {13} ,0} \right)\) \(e = \frac{{\sqrt {13} }}{2}\) If \(e\), \(2\) the eccentricity of the ellipse, then…
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