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Find the coordinates of the centre of the circle passing through the points (0, 0), (-2, 1) and (-3, 2). Also, find its radius.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM

Let P(x, y) be the centre of the circle passing through the points O(0, 0), A(-2, 1) and B(-3, 2). Then,

OP = AP = BP

Now, OP = AP OP2 = AP2

x2 + y2 = (x + 2)2 + (y - 1)2

x2 + y2 = x2 + y2 + 4x - 2y + 5

4x - 2y + 5 = 0 ...(i)

Now, OP = BP OP2 = BP2

x2 + y2 = (x + 3)2 + (y - 2)2

x2 + y2 = x2 + y2 + 6x - 4y + 13

6x - 4y + 13 = 0 ...(ii)

On solving equations (i) and (ii), we get x = and y =

Thus, the coordinates of the centre are

Answered by | 04 Jun, 2014, 03:23: PM

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