the equation of a circle that has a center at (h,k) and radius of r is
(x-h)²+(y-k)²=r²
so given center (-5,-7)
(x-(-5))²+(y-(-7))²=r²
(x+5)²+(y+7)²=r²
passes through (0,0)
sub the point to find r
(0+5)²+(0+7)²=r²
25+49=r²
74=r²
the equation is
(x+5)²+(y+7)²=74 or equivilently
(x+5)²+(y+7)²=(√74)²
