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 1 (b) 2 (c) `5/(16)` (d) 5

The length of the perpendicular from the focus s of the parabola y^(2)=4ax on the tangent at P is

Let F be the focus of the parabola y^(2)=4ax and M be the foot of perpendicular form point P(at^(2), 2at) on the tangent at the vertex. If N is a point on the tangent at P, then (MN)/(FN)"equals"

If Q is the foot of the perpendicular from P(2, 4,3] on the line joining the points (1,2,4] and B(3,4,5} , then the coordinates of Q are

If the tangents at the points P and Q on the parabola y^2 = 4ax meet at R and S is its focus, prove that SR^2 = SP.SQ .

P and Q are two distinct points on the parabola,y^(2)=4x with parameters t and t_(1) respectively.If the normal at P passes through Q, then the minimum value of t_(1)^(2) is

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 sires of the parateral triangle SMP(where S is the focus of the parabola),is

If PQ is the focal chord of the parabola y^(2)=-x and P is (-4, 2) , then the ordinate of the point of intersection of the tangents at P and Q is

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.