If the latus rectum of an ellipse is equal to | vedclass

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(B) The formula for the length of the latus rectum of an ellipse is $\frac{2b^2}{a}$.Given that the latus rectum is equal to half of the minor axis $(

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

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(B) The formula for the length of the latus rectum of an ellipse is $\frac{2b^2}{a}$.Given that the latus rectum is equal to half of the minor axis $(2b)$,we have:$\frac{2b^2}{a} = \frac{1}{2} 	imes (2b)$$\frac{2b^2}{a} = b$Dividing both sides by $b$ (since $b 
eq 0$):$\frac{2b}{a} = 1 \implies \frac{b}{a} = \frac{1}{2}$Squaring both sides:$\frac{b^2}{a^2} = \frac{1}{4}$The eccentricity $e$ of an ellipse is given by $e = \sqrt{1 - \frac{b^2}{a^2}}$.Substituting the value of $\frac{b^2}{a^2}$:$e = \sqrt{1 - \frac{1}{4}} = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}$.

If the latus rectum of an ellipse is equal to half of its minor axis,then its eccentricity is

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