JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
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 :
- A \(\frac{4}{\sqrt{17}}\)
- B \(\frac{\sqrt{3}}{16}\)
- C \(\frac{3}{\sqrt{19}}\)
- D \(\frac{\sqrt{5}}{7}\)
Answer & Solution
Correct Answer
(A) \(\frac{4}{\sqrt{17}}\)
Step-by-step Solution
Detailed explanation
\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 \\ &…
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