Let the circle S : 36x² + 36y² $$-$$ 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x $$-$$ 2y = 4 and 2x $$-$$ y = 5 lies inside the circle S, then :

Let r₁ and r₂ be the radii of the largest and smallest circles, respectively, which pass through the point ($$-$$4, 1) and having their centres on the circumference of the circle x² + y² + 2x + 4y $$-$$ 4 = 0. If $${{{r_1}} \over {{r_2}}} = a + b\sqrt 2 $$, then a + b is equal to :

Let S₁ : x² + y² = 9 and S₂ : (x $$-$$ 2)² + y² = 1. Then the locus of center of a variable circle S which touches S₁ internally and S₂ externally always passes through the points :

Choose the correct statement about two circles whose equations are given below :

x² + y² $$-$$ 10x $$-$$ 10y + 41 = 0

x² + y² $$-$$ 22x $$-$$ 10y + 137 = 0