Q. The latusractum of the hyperbola $9x^{2} - 16y^{2} + 72x - 32 - 16 = 0$ is
A) $\frac{9}{2}$
B) $- \frac{9}{2}$
C) $\frac{32}{3}$
D) $- \frac{32}{3}$
Explanation
(a)
Given equation can be rewritten as
$9\left\lbrack (x + 4 \right)^{2} - 16\rbrack - 16\left\lbrack (y + 1)^{2} - 1 \right\rbrack - 16 = 0$
$\Rightarrow \ \ \ \frac{(x + 4)^{2}}{16} - \frac{(y + 1)^{2}}{9} = 1$
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.