The length of the latus rectum of the ellipse | vedclass

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(B) Given the equation of the ellipse is $\frac{x^2}{36} + \frac{y^2}{49} = 1$.Comparing this with the standard form $\frac{x^2}{a^2} + \frac{y^2}{b^2

Vedclass · Accepted Answer

$72/7$

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(B) Given the equation of the ellipse is $\frac{x^2}{36} + \frac{y^2}{49} = 1$.Comparing this with the standard form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,we have $a^2 = 36$ and $b^2 = 49$.Since $b^2 > a^2$,the major axis is along the $y$-axis,so $b = 7$ and $a = 6$.The length of the latus rectum for an ellipse with the major axis along the $y$-axis is given by $\frac{2a^2}{b}$.Substituting the values,we get $	ext{Length} = \frac{2 	imes 36}{7} = \frac{72}{7}$.

The length of the latus rectum of the ellipse $\frac{x^2}{36} + \frac{y^2}{49} = 1$ is:

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