Question

If the line $x-y-1=0$ intersect the parabola $y^2=8x$ at P & Q then find the point of intersection of tangents at P & Q

Answer 1

Let (h, k) be point of intersection of tangents then chord of contact is
$yk=4(x+h)$
$4x-yk+4h=0$ ...........(i)
But given is $x-y-1=0$
$\therefore \frac{4}{1}=\frac{-k}{-1}=\frac{4h}{-1}\Rightarrow h=-1,k=4$
$\therefore point\equiv (-1,4)$