The tangent at P(`at^2, 2at`) to the parabola `y^(2)=4ax` intersects X axis at A and the normal at P meets it at B then area of triangle PAB is

The tangent at any point P onthe parabola y^2=4a x intersects the y-axis at Qdot Then tangent to the circumcircle of triangle P Q S(S is the focus) at Q is a line parallel to x-axis y-axis a line parallel to y-axis (d) none of these

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

The tangent to the hyperbola xy=c^2 at the point P intersects the x-axis at T and y- axis at T'.The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N' . The areas of the triangles PNT and PN'T' are Delta and Delta' respectively, then 1/Delta+1/(Delta)' is

The tangent and normal at the point p(18, 12) of the parabola y^(2)=8x intersects the x-axis at the point A and B respectively. The equation of the circle through P, A and B is given by

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 a tangent to the parabola y^2 = 4ax meets the axis of the parabola in T and the tangent at the vertex A in Y, and the rectangle TAYG is completed, show that the locus of G is y^2 + ax = 0.

Tangent PT and normal PN to the parabola y^(2)=4ax at a point P on it meet its axis at T and N respectively. The Locus of the centroid of the triangle PTN is a parabola whose

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

If a tangent to the parabola y^2=4a x meets the x-axis at T and intersects the tangents at vertex A at P , and rectangle T A P Q is completed, then find the locus of point Qdot

If a tangent to the parabola y^2=4a x meets the x-axis at T and intersects the tangents at vertex A at P , and rectangle T A P Q is completed, then find the locus of point Qdot