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10.2 parabola,ellipse,hyperbola — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.2 parabola,ellipse,hyperbola1 Mark
MCQ
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
  • ✓
    $4$
  • B
    $2\sqrt 2$
  • C
    $4\sqrt 2$
  • D
    $2$
✓

Answer

Correct option: A.
$4$
a
${m_{SB}}.{m_{S'B}} = 1$

${b^2} = {a^2}{e^2}\,\,\,\,\,\,\,\,.......\left( i \right)$

$\frac{1}{2}S'B.SB = 8$

${a^2}{e^2} + {b^2} = 16\,\,\,\,\,\,\,\,.......\left( {ii} \right)$

${b^2} = {a^2}\left( {1 - {e^2}\,} \right)\,\,\,\,\,\,\,\,.......\left( {iii} \right)$

using $(i),(ii),(ii)$ $a = 4$

$b = 2\sqrt 2 $

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

$\therefore \ell \left( {L.R} \right) = \frac{{2{b^2}}}{a} = 4$

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