Let the foci of a hyperbola be (1,14) and (1,-12).

Question

Let the foci of a hyperbola be $(1,14)$ and $(1,-12)$. If it passes through the point $(1,6)$, then the length of its latus-rectum is :

Accepted Answer

$\begin{aligned} & \mathrm{be}=13, \mathrm{~b}=5 \ & \mathrm{a}^2=\mathrm{b}^2\left(\mathrm{e}^2-1ight) \ & =\mathrm{b}^2 \mathrm{e}^2-\mathrm{b}^2 \ & =169-25=144 \ & \ell(\mathrm{LR})=\frac{2 \mathrm{a}^2}{\mathrm{~b}}=\frac{2 	imes 144}{5}=\frac{288}{5}\end{aligned}$

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