Verified Solution • 2025–26 Session moderate

QJEEM19Ma1581: JEE Main 2019 Mathematics - Class 11 JEEM19Ma1581 Solution: Let S and S' be the foci of an ellipse and B be any one of the…

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

Δ

S'BS is a right angled triangle with right angle at B and area (

Δ

S'BS) = 8 sq. units, then the length of a latus rectum of the ellipse is :

Step-by-Step Verified Solution

b² = a²e² . . . . . . (i)

\frac{1}{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 =

\frac{1}{\sqrt{2}}

∴

ℓ

(L.R)

=

\frac{2 b^{2}}{a} = 4