Q20 of 53 Page 122

Find the coordinates of the centre of the circle passing through the points P(6,-6), Q(3,-7)and R(3,3).

According to the distance formula, the distance 'd' between two points (a,b) and (c,d) is given by
 .....(1)


Let the centre be A(x,y)


As it passes through the given points, distance between centre and the points is the radius.


AP =


AQ =


AR =


As AP = AQ


Squaring both sides


(x-6)2 + (y + 6)2 = (x-3)2 + (y + 7)2


Simplifying


12y-12x + 72 = 14y-6x + 58


2y + 6x-14 = 0... (a)


AP = AR


Squaring both sides and simplifying


6y-6x + 54 = 0 ...(b)


Solving for x and y using (a) and (b)


We get x = 3; y = -2


Hence centre is (3,-2)


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