Question

From a point on the line $x-y+2=0$ tangents are drawn to the hyperbola $\frac{x^2}{6}-\frac{y^2}{2}$ = 1 such that the chord of contact passes through a fixed point $(\lambda ,\mu )$ Then $\frac{\lambda }{\mu }$ is equal to :

Answer 1

let any point on the line be $(a,a+2)$

Then chord of contact is given by $S_1=0$

$\Rightarrow \frac{ax}{6}-\frac{(a+2)y}{2}=1$

$\Rightarrow 6(y+1)-a(x-3y)=0$

It represents family of straight lines passing through point of intersection of $y=-1$ and $x=3y$

$\Rightarrow \lambda =-3$ and $\mu =-1$

Hence, $\frac{\lambda }{\mu }=3$