The length of the latus rectum of the ellipse | vedclass

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(D) Given the equation of the ellipse is $5x^2 + 9y^2 = 45$.Dividing both sides by $45$,we get $\frac{x^2}{9} + \frac{y^2}{5} = 1$.Comparing this with

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$10/3$

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(D) Given the equation of the ellipse is $5x^2 + 9y^2 = 45$.Dividing both sides by $45$,we get $\frac{x^2}{9} + \frac{y^2}{5} = 1$.Comparing this with the standard form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,we have $a^2 = 9$ and $b^2 = 5$,which implies $a = 3$ and $b = \sqrt{5}$.The length of the latus rectum of an ellipse is given by the formula $\frac{2b^2}{a}$.Substituting the values,we get $	ext{Latus rectum} = \frac{2 	imes 5}{3} = \frac{10}{3}$.

The length of the latus rectum of the ellipse $5x^2 + 9y^2 = 45$ is

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