Find the equation of a circle which passes through the points (2, –2), and (3, 4) and whose centre lies on the line x + y = 2.

Hello student,
Please find the answer to your question below
Let the equation of a circle is
x²+y²+2gx+2fy+c=0
Given it passes through (2,-2) and (3,4)
Hence by substituting the pts in equation of circle we get
4g-4f+c=-8.....(1)
6g+8f+c=-25.....(2)
subtracting 1 from 2 we get
-2g-12f=17..........(3)
also given center lies on x+y=2
So -g-f=2..........(4)
solving 3,4 we get g=-7/10,f=-13/10 and c=-104/10
By substituting above values in circle equation we get
The equation of a circle which passes through the points (2, –2), and (3, 4) and whose centre lies on the line x + y = 2 is
10x²+10y²-14x-26y-104=0