Question

Find the coordinates of O, the centre passing through A( -2, -3), B(-1, 0) and C(7, 6). Also, find its radius. 

Answer 1

let o (x, y) be the centre of the circle.

OA = OB       (radii of square circle)

⇒ OA² = OB² 

(x + 2)² + (y + 3)² = (x + 1)² + (y - 0)²

⇒ x² + 4 + 4x + y² + 9 + 6y = x² + 1 + 2x + y²

⇒ 2x + 6y + 12 = 0 

⇒ x + 3y + 6 = 0  .........(1)

Similarly, OB=OC 

⇒ OB² =OC² 

(x + 1)² + (y + 0)² = (x + 7)² + (y - 6)²

⇒ x² + 1 + 2x + y² = x² + 49 - 14x + y² + 36 +12y 

⇒ 16x - 12y - 84 = 0

⇒ 4x - 3y - 21 = 0 .... (2)

⇒ 4x + 12y +24 = 0 .....(1)

on solving (1)& (2) we get, 

- 15 y - 45 = 0

⇒ y = -3

from (1)

x - 9 + 6 = 0

⇒ x = 3

Thus coordinate of O are (3 , -3)

Radius  =`sqrt ((3 + 2)^2 + (- 3 + 3)^2)`

`= sqrt (25 + 0)`

` = sqrt 25` units

= 5 units