Q. 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 :
A) $\frac{24}5$
B) $\frac{25}6$
C) $\frac{144}5$
D) $\frac{288}5$
Explanation
[Solution by Dr. Abubacker] $2c=26$, so $c=13$. For $P(1,6)$: $|PF_1-PF_2|=|8-18|=10=2a$, so $a=5$ and $b^2=169-25=144$. Latus rectum $=\frac{2b^2}{a}=\frac{288}5$. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.