find the coordinates of the center of circle passing through the points{o,o},{-2,1) and(-3,2)plz explain step wise

Let the given points be O(0, 0), A(-2, 1) and B(-3, 2).

Let X (x, y) be the centre of the circle.

Since, points O, A, B lie on the boundary of the circle, so,

OX = AX = BX

or, OX² = AX² = BX²

 

Now, OX² = AX²

So, we have:

x² + y² = (x + 2)² + (y - 1)²

x² + y² = x² + 4 + 4x + y² + 1 - 2y

4x - 2y + 5 = 0          ... (i)

 

Now, OX² = BX²

So, we have:

x² + y² = (x + 3)² + (y - 2)²

x² + y² = x² + 9 + 6x + y² + 4 - 4y

6x - 4y + 13 = 0          ... (ii)

 

Now, we solve equation (i) and (ii) to get the values of x and y.

From (1), 12 have:

8x - 4y + 10 = 0

Subtracting (ii) from this equation,

2x - 3 = 0

x = 3/2

 

Now, from (i), we have:

2y = 4x + 5 = 11

y = 11/2

 

Thus, the coordinates of the centre of the circle are (3/2, 11/2).