TS EAMCET 18-July-2022 Shift 1 Solved Paper

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