Question

Find the centre of a circle passing through the points (6,-6), (3,-7) and (3,3)​

Answer 1

Let us assume

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

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

If O = (x, y) then

OA =OB =OC

Now will choose OA = OB, we have

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

Similarly: OB = OC

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

(y + 7)2 = (y – 3)2

y2 + 14y + 49 = y2 – 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

Answer

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

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