Let P be a point on (2, 0) and Q be a variable point on (y $$-$$ 6)² = 2(x $$-$$ 4). Then the locus of mid-point of PQ is

AB is a chord of a parabola y² = 4ax, (a > 0) with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis of the parabola is

From the point ($$-$$1, $$-$$6), two tangents are drawn to y² = 4x. Then the angle between the two tangents is

Let the tangent and normal at any point P(at², 2at), (a > 0), on the parabola y² = 4ax meet the axis of the parabola at T and G respectively. Then the radius of the circle through P, T and G is