Question

Let S and S' be the foci of the ellipse and B be any one of the extremities of its minor axis. If '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 :

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

Answer 1

Answer: (C)

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