Q. The eccentricity of the ellipse $9x^{2} + 5y^{2} - 18x - 20y - 16 = 0$ is
A) $\frac{1}{2}$
B) $\frac{2}{3}$
C) $\frac{3}{2}$
D) 2
Explanation
(b)
Given equation can be rewritten as
$9(x - 1)^{2} + 5(y - 2)^{2} = 45$
$\Rightarrow \ \frac{(x - 1)^{2}}{5} + \frac{(y - 2)^{2}}{9} = 1$
$\therefore Eccentricity,\ e = \ \sqrt{1 - \frac{a^{2}}{b^{2}}} = \sqrt{1 - \frac{5}{9}} = \frac{2}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.