Question 969153


to isolate {{{y}}} on {{{x^2+y^2-2y=0}}},   move {{{x^2}}} to the right and complete the square for {{{y}}}

{{{y^2-2y=0-x^2}}}

{{{(y^2-2y+_)-_=-x^2}}}....recall the rule {{{a^2-2ab+b^2=(a-b)^2}}}

in your case {{{a=1}}} and {{{2ab=2}}}=>{{{2*1b=2}}}=>{{{b=1}}}

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

{{{(y-1)^2-1=-x^2}}}

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

{{{y-1=sqrt(-x^2+1)}}}

{{{y=sqrt(-x^2+1)+1}}}