Question

If $d$ is the length of the tangent from the point $(100,81)$ to the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$, then $\frac{d^2}{538}$ is equal to

Answer 1

$d^2=S_{11}=\frac{100\times 100}{4}+\frac{81\times 81}{9}-1=3228$, when $S=0$ is equation of tangent.

$\therefore \frac{d^2}{538}=6$