KVPY 2020-21 SB SX Exam Previous Papers

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Question : 11 of 120

Marks: +1, -0

Let

{x^{2}}/{a^{2}}+{y^{2}}/{b^{2}}=1(b < a)

, be an ellipse with major axis

{AB}

and minor axis

{CD}

. Let

{F}_{1}

and

{F}_{2}

be its two foci, with

{A}, {F}_{1}, {F}_{2}, {B}

in that order on the segment

{AB}

. Suppose

\∠{F}_{1} {CB}=90°

. The eccentricity of the ellipse is

${\√{3}-1}/{2}$
${1}/{\√{3}}$
${\√{5}-1}/{2}$
${1}/{\√{5}}$

Solution:

{{b}}/{-{ae}} \×{{b}}/{{a}}=-1

\⇒{b}^{2}={a}^{2} {e}

\⇒{a}^{2}(1-{e}^{2})={a}^{2} {e}

\⇒{e}^{2}+{e}-1=0

\⇒{e}={-1+\√{5}}/{2}

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