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Question

Centre of the circle passing through the points (6,-6), (3,-7) and (3,3) is .

A
(3 , 2)
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B
(2 , 3)
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C
(3 , -2)
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Solution

The correct option is C (3 , -2)
Let the centre of the circle be P(x,y).
Distance from P to A,B and C is given by
AP =(x6)2+(y+6)2
BP = (x3)2+(y+7)2
CP=(x3)2+(y3)2

PA = PB (Radii of the same circle)
(x6)2+(y+6)2=(x3)2+(y+7)2
x2+3612x+y2+36+12y=x2+96x+y2+49+14y
6x2y+14=03x+y=7(i)
Similarly, PA = PC
(x6)2+(y+6)2=(x3)2+(y3)2
x2+3612x+y2+36+12y=x2+96x+y2+96y
6x+18y+54=03x+9y=27(ii)

On adding (i) and (ii),
we get 10y = -20 y=2 and x=3
The centre of the circle is (3 , -2).

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