Question

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

• A. $2\sqrt{2}$
• B. $2$
• C. $4$
• D. $4\sqrt{2}$

Answer 1

Answer: (C)

$4$

$m_{SB}.m_{SB}=-1$

$b^2=a^2{e}^2$ ........ (i)

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

$S^{\prime }B.SB=16$

$a^2{e}^2+b^2=16$ ......(ii)

$b^2=a^2(1-e^2)$ ....(iii)

using (i), (ii), (iii) $a=4$

$b=2\sqrt{2}$

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

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