If two tangents drawn from a point $P$ to the parabola $y^2=16(x-3)$ are at right angles.

Given the equation of parabola $y^2=16(x-3)$

Then, the locus point is $P$

Locus is directrix of parabola is $x+a=0$
$x-3+4=0$

$x+1=0$