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

Let A be the centre of the circle $${x^2} + {y^2} - 2x - 4y - 20 = 0$$. Let B(1, 7) and D(4, $$-$$2) be two points on the circle such that tangents at B and D meet at C. The area of the quadrilateral ABCD is