Q. If $e$ and $e_{1}\$are the eccentricities of hyperbolas $xy = c^{2}$ and $x^{2} - \ y^{2} = c^{2}$, then$\ e^{2} + \ e_{1}^{2}$ is
A) 1
B) 4
C) 6
D) 8
Explanation
(b)
Since, both the given hyperbolas are rectangular hyperbolas
$\therefore\ e = \sqrt{2},\ e_{1} = \sqrt{2}$
Hence, $e^{2} + e_{1}^{2} = 2 + 2 = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.