If `P(t^2,2t),t in [0,2]` , is an arbitrary point on the parabola `y^2=4x ,Q` is the foot of perpendicular from focus `S` on the tangent at `P ,` then the maximum area of ` P Q S` is (a)1 (b) 2 (c) `5/(16)` (d) 5

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 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 P be a point on the parabola y^2=3(2x-3) and M is the foot of perpendicular drawn from the point P on the directrix of the parabola, then length of each sides of an equilateral triangle SMP(where S is the focus of the parabola), is

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

y=x+2 is any tangent to the parabola y^2=8xdot The point P on this tangent is such that the other tangent from it which is perpendicular to it is (a) (2,4) (b) (-2,0) (c) (-1,1) (d) (2,0)

P and Q are any two points on the circle x^2+y^2= 4 such that PQ is a diameter. If alpha and beta are the lengths of perpendiculars from P and Q on x + y = 1 then the maximum value of alphabeta is

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)

Tangents are drawn to the hyperbola 4x^2-y^2=36 at the points P and Q. If these tangents intersect at the point T(0,3) then the area (in sq units) of triangle PTQ 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 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