Let the equation x² + y² + px + (1 $$-$$ p)y + 5 = 0 represent circles of varying radius r $$\in$$ (0, 5]. Then the number of elements in the set S = {q : q = p² and q is an integer} is __________.

The locus of a point, which moves such that the sum of squares of its distances from the points (0, 0), (1, 0), (0, 1), (1, 1) is 18 units, is a circle of diameter d. Then d² is equal to _____________.

The minimum distance between any two points P₁ and P₂ while considering point P₁ on one circle and point P₂ on the other circle for the given circles' equations

x² + y² $$-$$ 10x $$-$$ 10y + 41 = 0

x² + y² $$-$$ 24x $$-$$ 10y + 160 = 0 is ___________.

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 ________