We will convert the general equation to the ordinary form \left [tex]\bf{( x-h \right )^{2}+\left ( y-k \right )^{2}=r^{2}}[/tex]; For this we follow the following steps:
We rewrite the equation by ordering the x and y and we complete the perfect square trinomials:
[tex]\bf{x^{2}-2x+1+y^{2}+4y+4=4+1+4 }[/tex]
Factor the perfect square trinomials:
[tex]\bf{(x-1)^{2}+(y+2)^{2}=9 }\\\bf{ \ \ \ \ \Rightarrow \ C(1,-2) y \ r=3 }[/tex]
