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JEE Main 20252 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
2 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Ellipse

JEE Main 2025 · 2 April · Evening Shift · Mathematics · Ellipse

If the length of the minor axis of an ellipse is equal to one...

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 :

Options

  1. A417\frac{4}{\sqrt{17}}
  2. B316\frac{\sqrt{3}}{16}
  3. C319\frac{3}{\sqrt{19}}
  4. D57\frac{\sqrt{5}}{7}

Correct answer

A. 417\frac{4}{\sqrt{17}}

Step-by-step solution

2 b=14(2ae)ba=e4e=1−b2a2e=1−e216e2(1+116)=1e=417\begin{aligned} & 2 \mathrm{~b}=\frac{1}{4}(2 \mathrm{ae}) \\ & \frac{\mathrm{b}}{\mathrm{a}}=\frac{\mathrm{e}}{4} \\ & \mathrm{e}=\sqrt{1-\frac{\mathrm{b}^2}{\mathrm{a}^2}} \\ & \mathrm{e}=\sqrt{1-\frac{\mathrm{e}^2}{16}} \\ & \mathrm{e}^2\left(1+\frac{1}{16}\right)=1 \\ & \mathrm{e}=\frac{4}{\sqrt{17}}\end{aligned}
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