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`.

At a point P on the parabola y^(2) = 4ax , tangent and normal are drawn. Tangent intersects the x-axis at Q and normal intersects the curve at R such that chord PQ subtends an angle of 90^(@) at its vertex. Then

The tangents to the parabola y^(2)=4ax at the vertex V and any point P meet at Q. If S is the focus,then prove that SP.SQ, and SV are in G.

IF the normals to the parabola y^2=4ax at three points P,Q and R meets at A and S be the focus , prove that SP.SQ.SR= a(SA)^2 .

The tangent drawn at any point of the curve sqrtx+sqrty = sqrta meets the OX and OY axes at points P and Q respectively, prove that OP+OQ = a.

If st = 1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

Tangents and normal drawn to the parabola y^2=4a x at point P(a t^2,2a t),t!=0, meet the x-axis at point Ta n dN , respectively. If S is the focus of theparabola, then S P=S T!=S N (b) S P!=S T=S N S P=S T=S N (d) S P!=S T!=S N