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The tangent and normal at P(t), for all ...

The tangent and normal at `P(t)`, for all real positive `t`, to the parabola `y^2= 4ax` meet the axis of the parabola in `T` and `G` respectively, then the angle at which the tangent at `P` to the parabola is inclined to the tangent at `P` to the circle passing through the points `P, T `and `G` is

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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.

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