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

Asked by Rutuja Mehta | 18th Jan, 2014, 07:27: PM

Expert Answer:

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).

Answered by  | 19th Jan, 2014, 05:03: PM

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