S and S¹ foci of an ellipse. B is one end of the minor axis. If $∠ {SBS}^{1}$ is a right angled isoscles triangle, then e =

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$\frac{1}{\sqrt{2}}$

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

answer is A.

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Detailed Solution

${({SS}^{1})}^{2} = (BS)^{2} + {({BS}^{1})}^{2} \Rightarrow 4 a^{2} e^{2} = 2 (a^{2} e^{2} + b^{2}) 2 a^{2} e^{2} = a^{2} \Rightarrow e = \frac{1}{\sqrt{2}}$

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