Question 146717
Using the equation {{{(x-h)^2+(y-k)^2=r^2}}} we can see that {{{h=3}}}, {{{k=-1}}} and {{{r=5}}}. So the equation is  {{{(x-3)^2+(y-(-1))^2=5^2}}} which simplifies to {{{(x-3)^2+(y+1)^2=25}}}



Now we need to expand and simplify {{{(x-3)^2+(y+1)^2=25}}} 


{{{(x-3)^2+(y+1)^2=25}}} Start with the given equation



{{{x^2-6x+9+(y+1)^2=25}}} Foil {{{(x-3)^2}}} to get {{{x^2-6x+9}}}



{{{x^2-6x+9+y^2+2y+1=25}}} Foil {{{(y+1)^2}}} to get {{{y^2+2y+1}}}



{{{x^2-6x+9+y^2+2y+1-25=0}}} Subtract 25 from both sides



{{{x^2+y^2-6x+2y-15=0}}} Combine like terms




So the equation is {{{x^2+y^2-6x+2y-15=0}}}