Answer:
Option C
Explanation:
if the line y=mx+c isa normal to the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ , then
$c^{2}=\frac{m^{2}(a^{2}-b^{2})^{2}}{a^{2}+b^{2}m^{2}}$
[Here , m=2, a2 =9 , and b2 =16]
$=\frac{2^{2}(9-16)^{2}}{9+16\times (2)^{2}}$
$=\frac{4\times 49}{9+64}=\frac{4\times 49}{73}=\frac{196}{73}$
$\therefore$ $c=\frac{14}{\sqrt{73}}$
