JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the length of the minor axis of ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :
- A \(\frac{\sqrt{5}}{3}\)
- B \(\frac{\sqrt{3}}{2}\)
- C \(\frac{1}{\sqrt{3}}\)
- D \(\frac{2}{\sqrt{5}}\)
Answer & Solution
Correct Answer
(D) \(\frac{2}{\sqrt{5}}\)
Step-by-step Solution
Detailed explanation
\( 2 \mathrm{~b}=\mathrm{ae} \) \( \frac{\mathrm{b}}{\mathrm{a}}=\frac{\mathrm{e}}{2} \) \( \mathrm{e}=\sqrt{1-\frac{\mathrm{e}^2}{4}}\) \( \mathrm{e}=\frac{2}{\sqrt{5}}\)
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