Let S and S,' be the foci of an ellipse a | vedclass

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Question

${m_{SB}}.{m_{S'B}} = 1$

${b^2} = {a^2}{e^2}\,\,\,\,\,\,\,\,.......\left( i \right)$

$\frac{1}{2}S'B.SB = 8$

${a^2}{e^2} + {b^2} = 16

Vedclass · Accepted Answer

$4$

Vedclass · Answer

${m_{SB}}.{m_{S'B}} = 1$

${b^2} = {a^2}{e^2}\,\,\,\,\,\,\,\,.......\left( i ight)$

$\frac{1}{2}S'B.SB = 8$

${a^2}{e^2} + {b^2} = 16\,\,\,\,\,\,\,\,.......\left( {ii} ight)$

${b^2} = {a^2}\left( {1 - {e^2}\,} ight)\,\,\,\,\,\,\,\,.......\left( {iii} ight)$

using $(i),(ii),(ii)$ $a = 4$

$b = 2\sqrt 2 $

$e = \frac{1}{{\sqrt 2 }}$

$	herefore \ell \left( {L.R} ight) = \frac{{2{b^2}}}{a} = 4$

Let $S$ and $S\,'$ be the foci of an ellipse and $B$ be any one of the extremities of its minor axis. If $\Delta S\,'BS$ is a right angled triangle with right angle at $B$ and area $(\Delta S\,'BS) = 8\,sq.$ units, then the length of a latus rectum of the ellipse is

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