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

\frac{\sqrt{3}}{2}

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\frac{1}{2}

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\frac{1}{2 \sqrt{2}}

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\frac{1}{\sqrt{2}}

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Solution

The correct option is B $\frac{1}{\sqrt{2}}$
Given,
$2 b = 2 a e$

$2 a \sqrt{(1 - e^{2})} = 2 a e$

$e^{2} = 1 - e^{2}$

$\Rightarrow e = \frac{1}{\sqrt{2}}$

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

The correct option is B 1√2Given,2b=2ae2a√(1−e2)=2aee2=1−e2⇒e=1√2

The correct option is B $\frac{1}{\sqrt{2}}$
Given,
$2 b = 2 a e$

$2 a \sqrt{(1 - e^{2})} = 2 a e$

$e^{2} = 1 - e^{2}$

$\Rightarrow e = \frac{1}{\sqrt{2}}$