`T P` and `T Q` are tangents to the parabola `y^2=4a x` at `P and Q ,` respectively. If the chord `P Q` passes through the fixed point `(-a ,b),` then find the locus of `Tdot`

T P and T Q are tangents to the parabola y^2=4a x at Pa n dQ , respectively. If the chord P Q passes through the fixed point (-a ,b), then find the locus of Tdot

P and Q are two distinct points on the parabola, y^2 = 4x with parameters t and t_1 respectively. If the normal at P passes through Q , then the minimum value of t_1 ^2 is

Tangents are drawn from the points on a tangent of the hyperbola x^2-y^2=a^2 to the parabola y^2=4a xdot If all the chords of contact pass through a fixed point Q , prove that the locus of the point Q for different tangents on the hyperbola is an ellipse.

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

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

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:

If the distances of two points P and Q from the focus of a parabola y^2=4x are 4 and 9,respectively, then the distance of the point of intersection of tangents at P and Q from the focus is

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 distance of two points P and Q on the parabola y^(2) = 4ax from the focus S are 3 and 12 respectively. The distance of the point of intersection of the tangents at P and Q from the focus S is