For a hyberbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, if the length of the transvere axis is 8 and the distance between the foci is $2 \sqrt{41}$, then the length of its latus rectum is

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Aicharya · Accepted Answer

Given, $2 a=8$ $\Rightarrow \quad a=4$ $	herefore \quad 2 a e=2 \sqrt{41}$ $\Rightarrow \quad a e=\sqrt{41}$ $\because \quad a^2 e^2=a^2+b^2$ $41=16+b^2$ $\Rightarrow \quad b^2=25$ Length of latus rectum $=\frac{2 b^2}{a}$ $=\frac{2 	imes 25}{4}=\frac{25}{2}$

For a hyberbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, if the length of the transvere axis is 8 and the…

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