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

For the four circles M, N, O and P, following four equations are given :

Circle M : x² + y² = 1

Circle N : x² + y² $$-$$ 2x = 0

Circle O : x² + y² $$-$$ 2x $$-$$ 2y + 1 = 0

Circle P : x² + y² $$-$$ 2y = 0

If the centre of circle M is joined with centre of the circle N, further center of circle N is joined with centre of the circle O, centre of circle O is joined with the centre of circle P and lastly, centre of circle P is joined with centre of circle M, then these lines form the sides of a :