The diameters of a circle are along 2x+y−7=0 andx+3y−11=0 . Then the equation of this circle, which also passes through (5,7) is:

Point of intersection of  2x+y−7=0,x+3y−11=0 is (2,3) 2x+y−7=0, x+3y−11=0 are diameters⇒  Centre=C (2,3)Circle passes through A(5,7)⇒  Radius=CP=9+16=5 ∴ the equation of the circle is (x−2)2+(y−3)2=52⇒x2+y2−4x−6y−12=0