Given circle passes through the points (1,2),(3,4) . If its centre lines on the line x−y+3=0 Then, slope of AB=
4−2
3−1
=1 Slope of line perpendicular to AB=−1
Mid-point of AB=(2,3) Equation of line perpendicular to AB and passing through mid-point of AB y−3=−1(x−2) Line L1:x+y=5⋅⋅⋅⋅⋅⋅⋅(i) Also, centre lies on line x−y=−3⋅⋅⋅⋅⋅⋅⋅(ii) Point of intersection of Eqs. (i) and (ii) is the centre of circle Centre, O(1,4) Rảdius =AO=√0+22=2