Without changing the direction of the axes, the origin is transferred to the point (2, 3). Then the equation x² + y² $$-$$ 4x $$-$$ 6y + 9 = 0 changes to

The angle between a pair of tangents drawn from a point P to the circle x² + y² + 4x $$-$$ 6y + 9sin²$$\alpha$$ + 13cos²$$\alpha$$ = 0 is 2$$\alpha$$. The equation of the locus of the point P is

If one of the diameter of the circle, given by the equation x² + y² + 4x + 6y $$-$$ 12 = 0, is a chord of a circle S, whose centre is (2, $$-$$ 3), the radius of S is

A chord AB is drawn from the point A(0, 3) on the circle x² + 4x + (y $$-$$ 3)² = 0, and is extended to M such that AM = 2AB. The locus of M is