Question

Which is an equation of a circle with center (-5,-7) The pass through the point (0,0)

Answer 1

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