The point of contact of the circles x^2+y^2+2 x+2 y+1=0 and x^2+y^2-2 x+2 y+1=0 is

Step-by-step solution

Given equation of circles are aligned S₁ & x^2+y^2+2 x+2 y+1=0 and S₂ x^2+y^2-2 x+2 y+1 & =0 aligned In circle S₁ , centre c₁=(-1,-1) , radius r₁= 1+1-1 =1 In circle S₂ , centre C₂=(1,-1) , radius r₂= 1+1-1 =1 Now, distance between two centre gathered C₁ C₂= (-1-1)^2+0 =2 gathered Here, we see that C₁ C₂=r₁+r₂ i.e., both circle touch externally. So, point of contact of circle S₁ and S₂= Mid-point of C₁ and C₂= ( -1+1 2 , -1-1 2 )=(0,-1)