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

If the plane x/2+y/3+z/6=1 cuts the axes of coordinates at points, A ,B ," and "C , then find the area of the triangle A B C

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 area of the region bounded by the parabola (y-2)^(2) = x- 1 , the tangent to the parabola at the point (2,3) and the x-axis is

Each side of triangle ABC is divided into three equal parts. Find the ratio of the are of hexagon P Q R S T U to the area of the triangle ABC.

y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A,B (a,0), and c are concyclic. Tangents to the parabola y^(2)=4x at A and C intersect at point D and tangents to the parabola y^(2)=-8(x-a) intersect at point E. Then the area of quadrilateral DAEC is

The tangent PT and the normal PN to the parabola y^2=4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whose:

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 :