Question

If normal of circle $x^2+y^2+6x+8y+9=0$ intersect the parabola $y^2=4x$ at P and Q then find the locus of point of intersection of tangent's at P and Q.

Answer 1

$y^2=4x$

$y{y}_1=2(x+x_1)$

$ky=2(x+h)$

$2x-ky+2h=0$

$-6+4k+2k=0$

$2h+4k=6$

$h+2k=3$