The tangents to the parabola `y^2=4a x` at the vertex `V` and any point `P` meet at `Q` . If `S` is the focus, then prove that `S PdotS Q ,` and `S V` are in GP.

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 .

If the tangents at the points P and Q on the parabola y^(2)=4ax meet at T, and S is its focus,the prove that ST,ST, and SQ are in GP.

Two tangents to the parabola y^(2) = 8x meet the tangent at its vertex in the points P & Q. If PQ = 4 units, prove that the locus of the point of the intersection of the two tangents is y^(2) = 8 (x + 2) .

The tangent at P to a parabola y^(2)=4ax meets the directrix at U and the latus rectum at V then SUV( where S is the focus)

Two mutually perpendicular tangents of the parabola y^(2)=4ax at the points Q_(1) and Q_(2) on it meet its axis in P_(1) and P_(2) . If S is the focus of the parabola, then the value of ((1)/(SP_(1))+(1)/(SP_(2)))^(-1) is equal

Let the tangent to the parabola S : y^(2) = 2x at the point P(2,-2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to :

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 .