If `S` be the focus and `SH` be perpendicular to the tangent at `P`, then prove that `H` lies on the tangent at the vertex and `SH^2 = OS.SP`, where `O` is the vertex of the parabola.

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

The equation of the tangent at the vertex of the parabola x^(2)+4x+2y=0, is

The point (0,4) and (0,2) are the vertex and focus of a parabola. Find the equation of the parabola.

If the tangent at P to the parabola y^(2) =7x is parallel to 6y -x + 11 =0 then square of the distance of P from the vertex of the parabola is _______ .

If the bisector of angle A P B , where P Aa n dP B are the tangents to the parabola y^2=4a x , is equally, inclined to the coordinate axes, then the point P lies on the tangent at vertex of the parabola directrix of the parabola circle with center at the origin and radius a the line of the latus rectum.

The locus of foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola y^2 = 4ax is

Find the equation of parabola whose focus is (0,1) and the directrix is x+2=0. Also find the vertex of the parabola.

If the focus of a parabola is (2, 3) and its latus rectum is 8, then find the locus of the vertex of the parabola.

If the parabola y^(2) = 4ax passes through the point (4, 1), then the distance of its focus the vertex of the parabola is

If the focus of a parabola is (2, 3) and its latus rectum is 8, then find the locus of the vertex of the parabola.