Question

The centre of a circle is (x+2,x-1). Find x if the circle passes through (2,-2) and (8,-2)

Answer 1

circle important property is its distance from center to circumference is constant
use this concept
let center O and (2,-2) is B and (8,-2) is C

hence
OB^2=OC^2
(x+1-2)^2+(x-1+2)^2=(x+1-8)^2+(x-1+2)^2

x^2-2x+1=x^2-14x+49

12x=48

x=4
hence center of circle (5,3)