Let the
location of the center (x,y)
let the
distance between center and point (5,5) = d₁
let the
distance between center and point (1,5) = d₂
let the
distance between center and point (1,1) = d₃
The
condition of the circle is d₁
= d₂ = d₃
Making
two equations to find x , y
d₁² = d₂²
∴
(x-5)²
+ (y-5)²
= (x-1)²
+ (y-5)²
∴
(x-5)² = (x-1)²
∴
x-5 = \pm (x-1) ⇒⇒⇒
positive sign unacceptable
∴
x-5 = -(x-1)
∴
x = 3
d₁² = d₃²
∴
(x-5)²
+ (y-5)²
= (x-1)²
+ (y-1)²
substituting
with x and simplifying the equation
∴
y = 3
∴center
= (3,3)
The correct choice will be (C)
Answer ⇒⇒⇒ C. (3, 3)
