Let S and S' be the foci of an ellipse and B be any one of the extremities of its minor ax…

Question

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

Accepted Answer

b2 = a2e2 . . . . . .   (i)

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

S'B.SB = 16

a2e2 + b2 = 16 . . . . .(ii)

b2 = a2 (1 - e2) . . . . .(iii)

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

b = $$2\sqrt 2 $$

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

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

Solutions · 1