Q. The equation to the hyperbola having its eccentricity 2 and the distance between its foci is 8, is
A) $\frac{x^{2}}{12} - \frac{y^{2}}{4} = 1$
B) $\frac{x^{2}}{4} - \frac{y^{2}}{12} = 1$
C) $\frac{x^{2}}{8} - \frac{y^{2}}{2} = 1$
D) $\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$
Explanation
(b)
Given, $e = 2,\ \ 2ae = 8$
$ae = 4\ \Rightarrow \ a = 2$
$b^{2} = a^{2}\left( e^{2} - 1 \right)\ \Rightarrow \ b^{2} = 4(4 - 1)$
$\Rightarrow \ \ b^{2} = 12$
$\therefore$ Equation of hyperbola is
$\frac{x^{2}}{4} - \frac{y^{2}}{12} = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.