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

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 :

Consider the parabola y^(2)=4x . Let P and Q be points on the parabola wher P(4,-4)andQ(9,6) . Let R be a point on the area of the parabola between P and Q. Then the area of DeltaPQR is largest when

Let A(3, 0) and B(4, 1) are two points on the parabola y=(x-3)^(2) , find a point on this parabola where its tangent is parallel to the chord AB.

Let A, B be two distinct points on the parabola y^(2)=4x . If the axis of the parabola touches a circle of radius r having AB as diameter, the slope of the line AB is

Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at the focus of the parabola. Then the tangents drawn to the parabola at Aa n dB will intersect at

Consider the parabola y^2 = 8x. Let Delta_1 be the area of the triangle formed by the end points of its latus rectum and the point P( 1/2 ,2) on the parabola and Delta_2 be the area of the triangle formed by drawing tangents at P and at the end points of latus rectum. Delta_1/Delta_2 is :

y_(1) and y_(2) and y_(3) are the ordinates of three points on the parabola y ^(2) = 4ax, then the area of the triangle formed by the points is-

The straight line 3x+4y-12=0 meets the coordinate axes at Aa n dB . An equilateral triangle A B C is constructed. The possible coordinates of vertex C

The mirror image of the parabola y^2= 4x in the tangent to the parabola at the point (1, 2) is:

Points A, B, C lie on the parabola y^2=4ax The tangents to the parabola at A, B and C, taken in pair, intersect at points P, Q and R. Determine the ratio of the areas of the triangle ABC and triangle PQR