Question 893015
x^2 + y^2-2x-2y-2=0 and x^2+y^2+2x+2y-2=0


{{{x^2 + y^2-2x-2y-2=0}}}
{{{x^2-2x+y^2-2y-2=0}}}
{{{x^2-2x+1-1+y^2-2y+1-1-2=0}}}
{{{(x-1)^2+(y-1)^2-4=0}}}
{{{highlight_green((x-1)^2+(y-1)^2=4)}}}



 {{{x^2+y^2+2x+2y-2=0}}}
{{{x^2+2x+y^2+2y-2=0}}}
{{{x^2+2x+1-1+y^2+2y+1-1-2=0}}}
{{{(x+1)^2+(y+1)^2-4=0}}}
{{{highlight_green((x+1)^2+(y+1)^2=4)}}}


The symmetry of this system indicates that intersections should occur on the line {{{y=-x}}}.


{{{graph(300,300,-4,4,-4,4,1-sqrt(4-(x-1)^2),1+sqrt(4-(x-1)^2),-1-sqrt(4-(x+1)^2),-1+sqrt(4-(x+1)^2))}}}


(-1,1) and (1,-1) work as the intersections.