$c = 2$, so $ae = 2$. Latus rectum $= \frac{2b^2}{a} = 6 \Rightarrow b^2 = 3a$
Also $b^2 = a^2 - c^2 = a^2 - 4$
$$3a = a^2 - 4 \Rightarrow a^2 - 3a - 4 = 0 \Rightarrow a = 4$$
$$e = \frac{c}{a} = \frac{2}{4} = \frac{1}{2}$$
Back to JEE Main 2022 Coordinate Geometry
JEE Main 2022 — Mathematics Coordinate Geometry
hard
mcq
2022
Official previous-year question
Verified 30 May 2026.
Question
The eccentricity of the ellipse whose foci are $(\pm 2, 0)$ and length of latus rectum is $6$ is:
Options
- A
$\frac{1}{\sqrt{2}}$
- B
$\frac{1}{2}$
- C
$\frac{1}{\sqrt{3}}$
- D
$\frac{2}{3}$
Solution
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