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Question -

Find the centre of acircle passing through points (6, -6), (3, -7) and (3, 3).



Answer -

Let A = (6, -6), B = (3, -7), C = (3, 3) arethe points on a circle.

If O is the centre, then OA = OB = OC (radiiare equal)

If O = (x, y) then

OA =

OB =

OC =

Choose: OA = OB, we have

After simplifying above, we get -6x = 2y – 14….(1)

Similarly: OB = OC

(x – 3)+ (y + 7)2 =(x – 3)2 + (y – 3)2

(y + 7)2 = (y – 3)2

y+ 14y + 49 = y–6y + 9

20y =-40

or y = -2

Substituting the value of y in equation (1),we get;

-6x = 2y – 14

-6x = -4 – 14 = -18

x = 3

Hence, centre of the circle located at point(3,-2).

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