If the tangents at the points `Pa n dQ` on the parabola `y^2=4a x` meet at `T ,a n dS` is its focus, the prove that `S P ,S T ,a n dS Q` are in GP.

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 P,S Q , and S V are in GP.

If the normals at P, Q, R of the parabola y^2=4ax meet in O and S be its focus, then prove that .SP . SQ . SR = a . (SO)^2 .

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot

if the normal at the point t_(1) on the parabola y^(2) = 4ax meets the parabola again in the point t_(2) then prove that t_(2) = - ( t_(1) + 2/t_(1))

Two mutually perpendicular tangents of the parabola y^2=4a x meet the axis at P_1a n dP_2 . If S is the focus of the parabola, then 1/(S P_1) is equal to 4/a (b) 2/1 (c) 1/a (d) 1/(4a)

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that t_2 2geq8.

If the normals to the parabola y^2=4a x at three points P ,Q ,a n dR meet at A ,a n dS is the focus, then S PdotS qdotS R is equal to a^2S A (b) S A^3 (c) a S A^2 (d) none of these

The tangent at any point P onthe parabola y^2=4a x intersects the y-axis at Qdot Then tangent to the circumcircle of triangle P Q S(S is the focus) at Q is

If a tangent to the parabola y^2=4a x meets the x-axis at T and intersects the tangents at vertex A at P , and rectangle T A P Q is completed, then find the locus of point Qdot

Prove that the length of the intercept on the normal at the point P(a t^2,2a t) of the parabola y^2=4a x made by the circle described on the line joining the focus and P as diameter is asqrt(1+t^2) .