Tangents of a parabola

The Circumcircle of the triangle formed by any three tangents to a parabola passes through

AB, AC are tangents to a parabola y^(2)=4ax . If l_(1),l_(2),l_(3) are the lengths of perpendiculars from A, B, C on any tangent to the parabola, then

If x+y=0,x-y=0 are tangents to a parabola whose focus is (1,2) Then the length of the latusrectum of the parabola is equal

Prove that perpendicular drawn from locus upon any tangent of a parabola lies on the tangent at the vertex

Two tangents on a parabola are x-y=0 and x+y=0. S(2,3) is the focus of the parabola. The length of latus rectum of the parabola is

the tangent to a parabola are x-y=0 and x+y=0 If the focus of the parabola is F(2,3) then the equation of tangent at vertex is