Show that the locus of the point of intersection of mutually perpendicular tangetns to a parabola is its directrix.

Statement-1: y+b=m_(1) (x+a) and y+b=m_(2)(x+a) are perpendicular tangents to the parabola y^(2)=4ax . Statement-2: The locus of the point of intersection of perpendicular tangents to a parabola is its directrix.

Statement-1: The tangents at the extrenities of a forcal of the parabola y^(2)=4ax intersect on the line x + a = 0. Statement-2: The locus of the point of intersection of perpendicular tangents to the parabola is its directrix

The locus of the point of intersection of the perpendicular tangents to the parabola x^(2)=4ay is

The ,locus of the point of intersection of two perpendicular tangents to the parabola y^(2)=4ax is

The locus of the point of intersection of the perpendicular tangents to the parabola x^(2)-8x+2y+2=0 is

Find the equation of the system of coaxial circles that are tangent at (sqrt(2), 4) to the locus of the point of intersection of two mutually perpendicular tangents to the circle x^2 + y^2 = 9 .