JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(E_{1}: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, \mathrm{a}\,>\,\mathrm{b} .\) Let \(\mathrm{E}_{2}\) be another ellipse such that it touches the end points of major axis of \(E_{1}\) and the foci \(E_{2}\) are the end points of minor axis of \(E_{1}\). If \(E_{1}\) and \(E_{2}\) have same eccentricities, then its value is :
- A \(\frac{-1+\sqrt{3}}{2}\)
- B \(\frac{-1+\sqrt{6}}{2}\)
- C \(\frac{-1+\sqrt{5}}{2}\)
- D \(\frac{-1+\sqrt{8}}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{-1+\sqrt{5}}{2}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{e}^{2}=1-\frac{\mathrm{b}^{2}}{\mathrm{a}^{2}} ....(1)\) \(\mathrm{e}^{2}=1-\frac{\mathrm{a}^{2}}{\mathrm{c}^{2}} ....(2)\) \(\Rightarrow \frac{\mathrm{b}^{2}}{\mathrm{a}^{2}}=\frac{\mathrm{a}^{2}}{\mathrm{c}^{2}}\)…
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