The length of the latus rectum of the ellipse | vedclass

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(C) The given equation of the ellipse is $9x^2 + 4y^2 = 1$.Dividing by $1$,we can rewrite it as $\frac{x^2}{(1/3)^2} + \frac{y^2}{(1/2)^2} = 1$.Here,$

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$\frac{4}{9}$

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(C) The given equation of the ellipse is $9x^2 + 4y^2 = 1$.Dividing by $1$,we can rewrite it as $\frac{x^2}{(1/3)^2} + \frac{y^2}{(1/2)^2} = 1$.Here,$a^2 = \frac{1}{9}$ and $b^2 = \frac{1}{4}$.Since $b > a$,the major axis is along the $y$-axis.The length of the latus rectum for an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with $b > a$ is given by $\frac{2a^2}{b}$.Substituting the values,we get $	ext{Length} = \frac{2 	imes (1/9)}{1/2} = \frac{2/9}{1/2} = \frac{4}{9}$.

The length of the latus rectum of the ellipse $9x^2 + 4y^2 = 1$ is

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