Show that length of perpendecular from focus 'S' of the parabola `y^(2)= 4ax` on the Tangent at P is `sqrt(OS.SP)`

Prove that the locus of the foot of the perpendicular drawn from the focus of the parabola y ^(2) = 4 ax upon any tangent to its is the tangent at the vertex.

Let x+y=k be a normal to the parabola y^(2)=12x . If p is the length of the perpendicular from the focus of the parabola onto this normal then 4k-2 p^(2) =?

Length of the shortest normal chord of the parabola y^2=4ax is

Focus of parabola y = ax^(2) + bx + c is

The length of the subnormal to the parabola y^(2)=4ax at any point is equal to

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

M is the foot of the perpendicular from a point P on a parabola y^2=4a x to its directrix and S P M is an equilateral triangle, where S is the focus. Then find S P .

M is the foot of the perpendicular from a point P on a parabola y^2=4a x to its directrix and S P M is an equilateral triangle, where S is the focus. Then find S P .

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

Show that the locus of point of intersection of perpendicular tangents to the parabola y^2=4ax is the directrix x+a=0.