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 (a)`S P=S T!=S N` (b) `S P!=S T=S N` (c)`S P=S T=S N` (d) `S P!=S T!=S N`

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)

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

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 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.

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 distance of two points P and Q on the parabola y^(2) = 4ax from the focus S are 3 and 12 respectively. The distance of the point of intersection of the tangents at P and Q from the focus S is

If the line passing through the focus S of the parabola y=a x^2+b x+c meets the parabola at Pa n dQ and if S P=4 and S Q=6 , then find the value of adot

Normal to a rectangular hyperbola at P meets the transverse axis at N. If foci of hyperbola are S and S', then find the value of (SN)/(SP).

M is the foot of the perpendicular from a point P on a parabola y^2=4a x to its directrix and S P M is an equilateral triangle, where S is the focus. Then find S P .

Tangent is drawn at any point (p ,q) on the parabola y^2=4a x .Tangents are drawn from any point on this tangant to the circle x^2+y^2=a^2 , such that the chords of contact pass through a fixed point (r , s) . Then p ,q ,r and s can hold the relation (A) r^2q=4p^2s (B) r q^2=4p s^2 (C) r q^2=-4p s^2 (D) r^2q=-4p^2s