JEE Main 2017 (Offline)Question 1
A hyperbola passes through the point $P(\sqrt2,\sqrt3)$ and has foci at $(\pm2,0)$. Then the tangent to this hyperbola at $P$ also passes through the point :
Hyperbola
Solution
$a^2+b^2=4$, $\frac2{a^2}-\frac3{b^2}=1$ give $a^2=1$, $b^2=3$. Tangent at $P$: $\sqrt2x-\frac{y}{\sqrt3}=1$, satisfied by $\left(2\sqrt2,3\sqrt3\right)$.