For the parabola $y^2 = 8x$,what is the position of the point $(2, 5)$?

The maximum number of common normals of $y^2=4ax$ and $x^2=4by$ is equal to

If one end of a focal chord of the parabola $y^2 = 16x$ is $(1, -4)$,find the other end.

$A$ circle of radius $4$,drawn on a chord of the parabola $y^2 = 8x$ as diameter,touches the axis of the parabola. Then,the slope of the chord is

If the vertex of a parabola is $(4,3)$ and its directrix is $3x+2y-7=0$,then the equation of the latus rectum of the parabola is

If two perpendicular tangents are drawn from a point $P$ to the parabola $y^2 = 4x$,find the locus of $P$.