Mathematics · Ellipse

JEE Main 2025 — 2 April, Evening Shift — Question 35

If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is:

Answer: B

$2 b=\frac{1}{4}(2 \mathrm{ae})$

$\Rightarrow b=\frac{\mathrm{ae}}{4}$

$\Rightarrow \frac{b^{2}}{a^{2}}=\frac{e^{2}}{16}$

$\Rightarrow \frac{17 e^{2}}{16}=1 \Rightarrow e=\frac{4}{\sqrt{17}}$

Answer key and solution verified before publishing.

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