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 :

(1) \(\frac{25}{6}\)

(2) \(\frac{24}{5}\)

(3) \(\frac{288}{5}\)

(4) \(\frac{144}{5}\)

Answer 1

Correct option is (3) \(\frac{288}{5}\)  

be = 13, b = 5

\(\mathrm{a}^{2}=\mathrm{b}^{2}\left(\mathrm{e}^{2}-1\right)\)

\(=b^{2} \mathrm{e}^{2}-\mathrm{b}^{2}\)

\(=169-25=144\)

\(\ell(\mathrm{LR})=\frac{2 \mathrm{a}^{2}}{\mathrm{~b}}=\frac{2 \times 144}{5}=\frac{288}{5}\)