Parabola: Tangent

Important Questions|Position Of Point Relative To A Parabola|Chord Joining Two Points|Line And Parabola|Tangent To The Parabola|Important Questions|OMR

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.

If S be the focus of the parabola and tangent and normal at any point P meet its axis in T and G respectively, then prove that ST=SG = SP .

The normal to the parabola y^(2)=4x at P(9, 6) meets the parabola again at Q. If the tangent at Q meets the directrix at R, then the slope of another tangent drawn from point R to this parabola is