All we need is the radius.
Rewrite the equation:
x^2-12x+36 + y^2+10y+25+15-(36+25)=0 (completing the squares).
(x-6)^2+(y+5)^2=61-15=46=r^2 where r is the radius. The centre of the circle is (6,-5).
The circumference is therefore 2(pi)r=2(pi)sqrt(46)=42.61 approx.