If two tangents drawn from a point $P$ to the parabola $y^2=4x$ are at right angles, then the locus of $P$ is:

For any parabola, the locus of the point of intersection of perpendicular tangents is its directrix.The given parabola is $y^2=4ax$ with $a=1$.The equation of the directrix is $x=-a$.Therefore, the locus is $x=-1$.