EllipseHardBloom L3
Question
An ellipse has $OB$ as semi minor axis, $F$ and $F^{'}$ its foci and the angle $FBF^{'}$ is a right angle, then the eccentricity of ellipse is :
Options
A.$\frac{1}{\sqrt{3}}$
B.$\frac{1}{4}$
C.$\frac{1}{2}$
D.$\frac{1}{\sqrt{2}}$
Solution
Sol.(d) (Slope of $BF^{'}$ ) (slope of $BF$ ) $= - 1$
$$\begin{matrix} & \ \Rightarrow \ \left( - \frac{b}{ae} \right)\left( \frac{b}{ae} \right) = - 1 \\ & \ \Rightarrow \ b^{2} = a^{2}e^{2} \\ & \ \Rightarrow \ a^{2}\left( 1 - e^{2} \right) = a^{2}e^{2} \\ & \ \Rightarrow \ e = \frac{1}{\sqrt{2}} \end{matrix}$$
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