The angle between the circles aligned &x²+y²+4 x+2 y+1=0 and &x²+y²-2 x+6 y-6=0 is aligned

Step-by-step solution

Let be the angle of intersection of two given circles having centres (-g,-f)=(-2,-1) and (-g₁,-f₁ )=(1,-3) respectively, then aligned &= | -2 g g₁-2 f f₁+c+c₁ 2 g²+f²-c g₁²+f₁²-c₁ | &= | -2(2)(-1)-2(1)(3)+1-6 2 4+1-1 1+9+6 | &= | 4-6-5 2(2)(4) |= ( 7 6 ) &= ⁻¹ ( 7 16 ) aligned