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

If the parabola y^(2) = 4ax passes through the point (4, 1), then the distance of its focus the vertex of the parabola 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 points (0,4)a n d(0,2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.