Q. If in a hyperbola, the distance between the foci is 10 and the transverse axis has length 8, then the length of its latusrectum is
A) 9
B) $\frac{9}{2}$
C) $\frac{32}{3}$
D) $\frac{64}{3}$
Explanation
(b)
Given, $2a = 8\$and$\ 2ae = 10$
$\Rightarrow \ e = \frac{10}{8} = \frac{5}{4}$
Now, $b^{2}\ = a^{2}\ \left( e^{2}\ - 1 \right) = 16\left( \frac{25}{16} - 1 \right) = 9$
$\Rightarrow \ b = \pm 3$
Hence, length of latusrectum $= \frac{2b^{2}}{a} = \frac{2 \times 9}{4} = \frac{9}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.