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 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 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 .

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.

if the tangent to the parabola y=x(2-x) at the point (1,1) intersects the parabola at P. find the co-ordinate of P.

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

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

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