JEE PYQ: Ellipse Question 26
Question 26 - 2019 (12 Jan Shift 1)
Let S and S’ be the foci of an ellipse and B be any one of the extremities of its minor axis. If $\triangle S’BS$ is a right angled triangle with right angle at B and area ($\triangle S’BS$) = 8 sq. units, then the length of the latus rectum of the ellipse is:
(a) 4 (b) $2\sqrt{2}$ (c) $4\sqrt{2}$ (d) 2
Show Answer
Answer: (a) 4
Solution
Slopes: $\frac{b}{-ae} \times \frac{b}{ae} = -1 \Rightarrow b^2 = a^2e^2$
Area: $\frac{1}{2} \cdot 2ae \cdot b = 8 \Rightarrow b^2 = 8$
$a^2e^2 = 8$, $a^2e^2 = a^2 - b^2 \Rightarrow 8 = a^2 - 8 \Rightarrow a^2 = 16$
Latus rectum $= \frac{2b^2}{a} = \frac{16}{4} = 4$
BETA
