The centre of the circle is midway between the endpoints of the diameter=((7+2)/2,(5-1)/2)=(9/2,2).
The length of the diameter is √((7-2)2+(5-(-1))2)=√(25+36)=√61. So the radius=√61/2.
The equation of the circle is (x-9/2)2+(y-2)2=61/4 (standard form).
Multiply through by 4: (2x-9)2+(2y-4)2=61 (removing fractions).