The angle between circles x^2+y^2+2 x+4 y+1=0 and x^2+y^2-2 x+6 y-3=0 is

Step-by-step solution

Circles are aligned & c₁, x^2+y^2+2 x+4 y+1=0 & c₂, x^2+y^2-2 x+6 y-3=0 aligned On comparing with general form of circles x^2+y^2+2 g x+2 f y+c=0 where, centre = (− g, − f) and radius gathered = g^2+f^2-c c₁=(-1,-2) and r₁= 1+4-1 =2 c₂=(1,-3) and r₂= 1+9+3 = 13 d=c₁ c₂= (-1-1)^2+(-2+3)^2 = 4+1 = 5 = | d^2-r₁^2-r₂^2 2 r₁ r₂ |= | 5-4-13 2 2 13 |= | -3 13 | = 3 13 = ⁻¹ ( 3 13 ) gathered