Q. The equation of the ellipse whose distance between foci is equal to 8 and distance between the directrix is 18, is
A) $5x^{2} - 9y^{2} = 180$
B) $9x^{2} + 5y^{2} = 180$
C) $x^{2} + 9y^{2} = 180$
D) $5x^{2} + 9y^{2} = 180$
Explanation
(d)
Given, $2ae = 8$ and $\frac{2a}{e} = 18$
$\Rightarrow \ a = \ \sqrt{4 \times 9} = 6$
$\therefore\ e = \frac{2}{3}$
Therefore, $b = 6\ \sqrt{\left( 1 - \frac{4}{9} \right)} = 2\sqrt{5}$
Hence, the required equation is $\frac{x^{2}}{36} + \frac{y^{2}}{20} = 1\$
$\Rightarrow \ 5x^{2} + 9y^{2} = 180$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.