Mathematics - Ellipse Question with Solution | TestHub

MathematicsEllipseGeneralMedium2 minPYQ_2021

MathematicsMediumsingle choice

An ellipse has $OB$ as semi minor axis, $F$ and $F^{'}$ its focii and the angle FBF' is a right angle. Then the eccentricity of the ellipse is

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Solution:

$∵ ∠ FBF^{'} = 9 0^{\circ}$ $\Rightarrow FB^{2} + F^{'} B^{2} = FF^{'2}$ $∴ (a^{2} e^{2} + b^{2})^{2} + (a^{2} e^{2} + b^{2})^{2} = (2 a e)^{2}$ $\Rightarrow 2 (a^{2} e^{2} + b^{2}) = 4 a^{2} e^{2}$ $\Rightarrow e^{2} = \frac{b ^{2}}{a ^{2}}$
Also $e^{2} = 1 - \frac{b ^{2}}{a ^{2}} = 1 - e^{2}$ $\Rightarrow 2 e^{2} = 1 \Rightarrow e = \frac{1}{2}$

Stream:BITSATSubject:MathematicsTopic:EllipseSubtopic:General

⏱ 2mℹ️ Source: PYQ_2021

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