TP and TQ are tangents to the parabola y^2 = 4ax The normals at P and Q intersect at R on the curve.. Find the locus of centre of circle circumscribing the triangle TPQ.

From a variable point R on the line y = 2x + 3 tangents are drawn to the parabola y^(2)=4ax touch it at P and Q point. Find the locus of the centroid of the triangle PQR.

Two tangents to the parabola y^2=4ax make supplementary angles with the x-axis. Then the locus of their point of intersection is

A variable tangent to the parabola y^(2)=4ax meets the parabola y^(2)=-4ax P and Q. The locus of the mid-point of PQ, is

A tangent to the parabola y^2 + 4bx = 0 meets the parabola y^2 = 4ax in P and Q. The locus of the middle points of PQ 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

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:

The tangents to the parabola y^2=4ax at P(at_1^2,2at_1) , and Q(at_2^2,2at_2) , intersect at R. Prove that the area of the triangle PQR is 1/2a^2(t_1-t_2)^3

If tangent at P and Q to the parabola y^2 = 4ax intersect at R then prove that mid point of R and M lies on the parabola, where M is the mid point of P and Q.

If a tangent to the parabola y^(2) = 4ax meets the x-axis in T and the tangent at the Vertex A in P and the rectangle TAPQ is completed then locus of Q is

From a point P, two tangents are drawn to the parabola y^(2) = 4ax . If the slope of one tagents is twice the slope of other, the locus of P is