Question

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

Answer 1

step1:- let center of circle =(a, b)
but center lies x+y=2
so, a+b=2
b=2-a
now center (a,2-a)
step 2:- because (2,-2) and (3,4) passing through circle
so,
(a-2)^2+(2-a+2)^2=(a-3)^2+(2-a-4)^2
{circle have constant radius i.e distance from circumference to center is always equal}
now solve above equation
a=0.7
2-a=1.3
now radius =root{(2-0.7)^2+(-2-1.3)^2}