Q. The equation of hyperbola whose foci are (2, 4) and $( - 2,4)$ and eccentricity is $\frac{4}{3},$ is
A) $x^{2} - (y - 4)^{2} = 5$
B) $\frac{x^{2}}{9} - \frac{(y - 4)^{2}}{7} = \frac{1}{4}$
C) $\frac{x^{2}}{9} - \frac{y^{2}}{7} = \frac{1}{4}$
D) None of these
Explanation
(b)
Given, eccentricity, $e = \frac{4}{3}$
Distance between foci $= 4 = 2\ ae\ \Rightarrow a^{2} = \frac{9}{4}$
$\therefore\ \ b^{2} = a^{2}\left( e^{2} - 1 \right) = \frac{9}{4}\left( \frac{16}{9} - 1 \right) = \frac{7}{4}$ and centre is $(0,\ 4).$
$\therefore\ \$Equation of hyperbola is $\frac{x^{2}}{9} - \frac{(y - 4)^{2}}{7} = \frac{1}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.