Q. The equation of the hyperbola referred to the axes of coordinate and whose distance between the foci is 16 and eccentricity is $\sqrt{2},$ is
A) $x^{2} - y^{2} = 16$
B) $x^{2} - y^{2} = 32$
C) $x = 2y^{2} = 16$
D) $y^{2} - x^{2} = 16$
Explanation
(b)
Given, $2ae = 16$ and $e = \sqrt{2}$
$\Rightarrow 2a\sqrt{2} = 16\ \Rightarrow a = 4\sqrt{2}$
$\because\ \ e = \sqrt{2},$ it means it is a rectangular hyperbola, where $a = b = 4\sqrt{2}$
$\therefore\ \$The equation of the hyperbola is $x^{2} - y^{2} = 32.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.