Let E_{1}: frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{ | vedclass

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Question

$\mathrm{e}^{2}=1-\frac{\mathrm{b}^{2}}{\mathrm{a}^{2}} ....(1)$

$\mathrm{e}^{2}=1-\frac{\mathrm{a}^{2}}{\mathrm{c}^{2}} ....(2)$

$\Rightarrow \

Vedclass · Accepted Answer

$\frac{-1+\sqrt{5}}{2}$

Vedclass · Answer

$\mathrm{e}^{2}=1-\frac{\mathrm{b}^{2}}{\mathrm{a}^{2}} ....(1)$

$\mathrm{e}^{2}=1-\frac{\mathrm{a}^{2}}{\mathrm{c}^{2}} ....(2)$

$\Rightarrow \frac{\mathrm{b}^{2}}{\mathrm{a}^{2}}=\frac{\mathrm{a}^{2}}{\mathrm{c}^{2}}$

$\Rightarrow \mathrm{c}^{2}=\frac{\mathrm{a}^{4}}{\mathrm{~b}^{2}} \Rightarrow \mathrm{c}=\frac{\mathrm{a}^{2}}{\mathrm{~b}}$

Also $b=c e$

$	herefore \frac{b}{e}=\frac{a^{2}}{b} \Rightarrow \frac{b^{2}}{a^{2}}=e$

$\quad e^{2}=1-b^{2} / a^{2} \Rightarrow e^{2}+e-1=0$

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