If S₁: x^2+y^2=4 and S₂: x^2+y^2-2 a x-2 b y+2=0 touches each other, then 4 times of radius of the circle S₂ is:

Step-by-step solution

aligned & C₁ C₂=r₁+r₂ & a^2+b^2 =2 a^2+b^2-2 & a^2+b^2=4+a^2+b^2 4 a^2+b^2-2 & 4 a^2+b^2-2 =2 & a^2+b^2-2 = 1 2 = r 2 & 4 r₂=2 & aligned