Question 202357
You need to get this equation into the standard form for a circle {{{(x-h)^2 + (y-k)^2 = r^2}}}

So you need to complete the squares for both x and y in your equation and see what comes from that
{{{x^2+6x+y^2-8y=-9}}}
{{{x^2+6x+9+y^2-8y=0}}}
{{{(x+3)^2 + y^2-8y=0}}}
{{{(x+3)^2 + y^2-8y+16=16}}}
{{{(x+3)^2 + (y-4)^2=16}}}

So r^2 = 16 --> r=4. Center is at (h,k) = (-3,4)

Here is a plot --> http://www30.wolframalpha.com/input/?i=x^2%2B6x%2By^2-8y%3D-9