Prove that the orthocentre of the triangle formed by any three tangents to a parabola lies on the directrix of the parabola

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

Prove that the portion of the tangent intercepted,between the point of contact and the directrix of the parabola y^(2)= 4ax subtends a right angle at its focus.

The centroid of the triangle formed by the feet of three normals to the parabola y^2=4ax

The area of triangle formed by tangent and normal at (8, 8) on the parabola y^(2)=8x and the axis of the parabola is

Consider the parabola y^2 = 8x. Let Delta_1 be the area of the triangle formed by the end points of its latus rectum and the point P( 1/2 ,2) on the parabola and Delta_2 be the area of the triangle formed by drawing tangents at P and at the end points of latus rectum. Delta_1/Delta_2 is :

The area of the triangle formed by three points on a parabola is how many times the area of the triangle formed by the tangents at these points?

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 equation of the directrix of the parabola x^(2) = 8y is

Prove that the line joining the orthocentre to the centroid of a triangle formed by the focal chord of a parabola and tangents drawn at its extremities is parallel to the axis of the parabola.

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