Diameyter of the circle :
2x+y-7=0 ....(i)
x+3y-11=0....(ii)
Diameter intesect at the centre of the circle
Equation (i) - 2xEquation (ii)
2x + y -7 -2x - 6y +22 =0
5y = 15
y =3
x = 11 - 3(3) = 2
Centre of the circle (2,3)
Equation of the circle
(x-2)2 + (y-3)2 = r2
Circle passes through point (5,7)
So (5-2)2 + (7-3)2 = r2
(3)2 + (4)2 = r2
r2 = 25
Equation of the circle : (x-2)2 + (y-3)2 = 25