SOLUTION: Graph the equation {{{x^2+y^2-6x+2y+1=0}}}

Algebra ->  Graphs -> SOLUTION: Graph the equation {{{x^2+y^2-6x+2y+1=0}}}       Log On


   

Question 140314: Graph the equation x%5E2%2By%5E2-6x%2B2y%2B1=0


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2By%5E2-6x%2B2y%2B1=0 Start with the given equation


x%5E2-6x%2By%5E2%2B2y%2B1=0 Rearrange the terms


x%5E2-6x%2By%5E2%2B2y=-1 Subtract 1 from both sides


%28x-3%29%5E2-9%2By%5E2%2B2y=-1 Complete the square for the x terms (let me know if you need help completing the square)


%28x-3%29%5E2-9%2B%28y%2B1%29%5E2-1=-1 Complete the square for the y terms


%28x-3%29%5E2%2B%28y%2B1%29%5E2-10=-1 Combine like terms


%28x-3%29%5E2%2B%28y%2B1%29%5E2=-1%2B10 Add 10 to both sides


%28x-3%29%5E2%2B%28y%2B1%29%5E2=9 Combine like terms


%28y%2B1%29%5E2=9-%28x-3%29%5E2 Subtract %28x-3%29%5E2 from both sides


y%2B1=0%2B-sqrt%289-%28x-3%29%5E2%29 Take the square root of both sides


y=0%2B-sqrt%289-%28x-3%29%5E2%29-1 Subtract 1 from both sides


So we have the two equations

y=sqrt%289-%28x-3%29%5E2%29-1 and y=-sqrt%289-%28x-3%29%5E2%29-1


When we graph the two, we get

Graph of y=sqrt%289-%28x-3%29%5E2%29-1 (red) and y=-sqrt%289-%28x-3%29%5E2%29-1(green)