Let `A = (9,6), B(4,-4)` be two points on parabola `y^2 = 4x` and `P(t^2,2t), t in [-2,3]` be a variable point on it such that area of triangle PAB is maximum, then P will be `A) (4,4) B) (3,-2sqrt3) C) (4,1) D) (1/4,1)`

If A(4,-4) and B(9,6) lies on y^2=4x and a point C on arc AOB (O= origin) such that the area of triangleACB is maximum then point c is (1) (1/4,1) (2) (1,1/4) (3) (1,1/2) (4) (1/2,1)

Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixed points on the parabola. Let C be a moving point on the parabola between Aa n dB such that the area of the triangle A B C is maximum. Then the coordinates of C are (a) (1/4,1) (b) (4,4) (c) (3,2/(sqrt(3))) (d) (3,-2sqrt(3))

Let A(4,-4) and B(9,6) be points on the parabola y^(2)=4x. Let C be chosen on the on the arc AOB of the parabola where O is the origin such that the area of DeltaACB is maximum. Then the area (in sq. units) of DeltaACB is :

Let (a,b) be a point on the parabola y=4x-x^(2) and is the point nearest to the point A(-1,4) Find (a+b).

The line x+2y=1 cuts the ellipse x^(2)+4y^(2)=1 1 at two distinct points A and B. Point C is on the ellipse such that area of triangle ABC is maximum, then find point C.

Let P(4,-4) and Q(9,6) be two points on the parabola, y^2=4x and let X be any point on the are POQ of this parabola, where O is the vertex of this parabola, such that the area of Delta PXQ is maximum. Then this maximum area (in square units) is (25k)/(4) . The value of k is

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

At what point on the parabola y^2=4x the normal makes equal angle with the axes? (A) (4,4) (B) (9,6) (C) (4,-4) (D) (1,+-2)

area of the triangle with vertices A(3,4,-1), B(2,2,1) and C(3,4,-3) is :