Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point ($$-$$5, 0). If the locus of the point P is a circle of radius r, then 4r² is equal to ________

If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle (x $$-$$ 2)² + (y $$-$$ 3)² = 25 at the point (5, 7) is A, then 24A is equal to _________.

If one of the diameters of the circle x² + y² - 2x - 6y + 6 = 0 is a chord of another circle 'C', whose center is at (2, 1), then its radius is ________.

Let PQ be a diameter of the circle x² + y² = 9. If $$\alpha $$ and $$\beta $$ are the lengths of the perpendiculars from P and Q on the straight line,
x + y = 2 respectively, then the maximum value of $$\alpha\beta $$ is _____.