Question 140314

{{{x^2+y^2-6x+2y+1=0}}} Start with the given equation



{{{x^2-6x+y^2+2y+1=0}}} Rearrange the terms



{{{x^2-6x+y^2+2y=-1}}}  Subtract {{{1}}} from both sides



{{{(x-3)^2-9+y^2+2y=-1}}} Complete the square for the x terms (let me know if you need help completing the square)



{{{(x-3)^2-9+(y+1)^2-1=-1}}} Complete the square for the y terms



{{{(x-3)^2+(y+1)^2-10=-1}}} Combine like terms



{{{(x-3)^2+(y+1)^2=-1+10}}} Add {{{10}}} to both sides



{{{(x-3)^2+(y+1)^2=9}}} Combine like terms



{{{(y+1)^2=9-(x-3)^2}}} Subtract {{{(x-3)^2}}} from both sides



{{{y+1=0+-sqrt(9-(x-3)^2)}}} Take the square root of both sides



{{{y=0+-sqrt(9-(x-3)^2)-1}}} Subtract 1 from both sides



So we have the two equations


{{{y=sqrt(9-(x-3)^2)-1}}} and {{{y=-sqrt(9-(x-3)^2)-1}}}



When we graph the two, we get


{{{ graph( 500, 500, -10, 10, -10, 10, sqrt(9-(x-3)^2)-1,-sqrt(9-(x-3)^2)-1  ) }}} Graph of {{{y=sqrt(9-(x-3)^2)-1}}} (red) and {{{y=-sqrt(9-(x-3)^2)-1}}}(green)