# CBSE Class 10 Answered

**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

Expert Answer

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 _{} OP^{2}
= AP^{2}

_{} x^{2} + y^{2} = (x + 2)^{2}
+ (y - 1)^{2}

_{} x^{2} + y^{2} = x^{2}
+ y^{2} + 4x - 2y + 5

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

Now, OP = BP _{} OP^{2}
= BP^{2}

x^{2} + y^{2} = (x
+ 3)^{2} + (y - 2)^{2}

x^{2} + y^{2 } = x^{2} + y^{2} + 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 _{}

Now, radius = OP = _{}

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

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