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) = 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

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.

.If the tangent to the parabola y 2 =4ax meets the axis in T and tangent at the vertex A in Y and the recatngle TAYG is completed, then the locus of G is

A tangent to the hyperbola x^(2)-2y^(2)=4 meets x-axis at P and y-aixs at Q. Lines PR and QR are drawn such that OPRQ is a rectangle (where O is origin).Find the locus of R.

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

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

Tangent and normal at any point P of the parabola y^(2)=4ax(a gt 0) meet the x-axis at T and N respectively. If the lengths of sub-tangent and sub-normal at this point are equal, then the area of DeltaPTN is given by

Tangent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the x-axis at point B and D , respectively. If the rectangle A B C D is completed, then the locus of C is (a)y=2a (b) y+2a=c (c)x=2a (d) none of these

A tangent is drawn to the parabola y^2=4a x at P such that it cuts the y-axis at Qdot A line perpendicular to this tangents is drawn through Q which cuts the axis of the parabola at R . If the rectangle P Q R S is completed, then find the locus of Sdot .

If the tangents at the points Pa n dQ on the parabola y^2=4a x meet at T ,a n dS is its focus, the prove that S P ,S T ,a n dS Q are in GP.