What are the coordinates of the center of the circle that passes through the points (1, 1), (1, 5), and (5, 5)? a. (0, 0) b. (5, 1) c. (3, 3) d. (2.5, 2.5)

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)

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get