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.

Prove that for all values of m, except zero the st. line $$y = mx + {a \over m}$$ touches the parabola y² = 4ax

Find the angle subtended by the double ordinate of length 2a of the parabola y² = ax at its vertex.