Find the centre of the circle passing through (2, 1), (5, - 8) and (2, - 9).

Coordinates of points on a circle are A(2,1), B(5,-8) and C(2,-9).

Let the coordinates of the centre of the circle be O(x, y)

Using distance formula =

Since the distance of the points A, B and C will be equal from the center, therefore

⇒ OA = OB

On squaring both sides, we get

⇒ x² + 4 - 4x + y² + 1 - 2y = x² + 25 - 10x + y² + 64 + 16y

⇒ 6x - 18y - 84 = 0

⇒ x - 3y - 14 = 0 ------------- (1)

Similarly, OC = OB

⇒ x² + 4 - 4x + y² + 81 + 18y = x² + 25 - 10x + y² + 64 + 16y

⇒ 6x - 2y - 4 = 0

⇒ 3x - y - 2 = 0 ------------- (2)

By solving equations (1) and (2), we get x = -1, y = -5

So, the coordinates of the centre of the circle is (-1, -5).

Radius of the circle = OA =

=

=

= units