Prove that the orthocentres of the triangles formed by three tangents and the corresponding three normals to a parabola are equidistant from the axis.

Tangents and Normals of a parabola

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

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

The locus of the Orthocentre of the triangle formed by three tangents of the parabola (4x-3)^(2)=-64(2y+1) is

Prove that for a given correspondence, if three angles of one triangles are congruent to the corresponding three angles of the other triangle, then the two triangles are similar.

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.

The locus of a point equidistant from three collinear points is