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`

Let PQ be a focal chord of the parabola y^2 = 4ax The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0 . Length of chord PQ is

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is

y=x is tangent to the parabola y=ax^(2)+c . If (1,1) is the point of contact, then a is

y=x is tangent to the parabola y=2ax^(2)+c . If (1,1) is the point of contact, then a is

Let PQ be a focal chord of the parabola y^(2)=4ax . The tangents to the parabola at P and Q meet at point lying on the line y=2x+a,alt0 . If chord PQ subtends an angle theta at the vertex of y^(2)=4ax , then tantheta=

The angle between tangents to the parabola y^2=4ax at the points where it intersects with teine x-y-a = 0 is (a> 0)

The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

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 :

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

The point of intersection of the tangents to the parabola y^(2)=4ax at the points t_(1) and t_(2) is -