Let B be the centre of the circle x² + y² $$-$$ 2x + 4y + 1 = 0. Let the tangents at two points P and Q on the circle intersect at the point A(3, 1). Then 8.$$\left( {{{area\,\Delta APQ} \over {area\,\Delta BPQ}}} \right)$$ is equal to _____________.

If the variable line 3x + 4y = $$\alpha$$ lies between the two
circles (x $$-$$ 1)² + (y $$-$$ 1)² = 1
and (x $$-$$ 9)² + (y $$-$$ 1)² = 4, without intercepting a chord on either circle, then the sum of all the integral values of $$\alpha$$ is ___________.

Two circles each of radius 5 units touch each other at the point (1, 2). If the equation of their common tangent is 4x + 3y = 10, and C₁($$\alpha$$, $$\beta$$) and C₂($$\gamma$$, $$\delta$$), C₁ $$\ne$$ C₂ are their centres, then |($$\alpha$$ + $$\beta$$) ($$\gamma$$ + $$\delta$$)| is equal to ___________.

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 __________.