Question

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

Answer 1

3) 2 A Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3).

Answer 2

Centre is (6,-2)

Step-by-step explanation:

Let A(6, -6), B(3, -7) and C(3, 3) be the points on the circle. Let P(x, y) be the  centre and PA, PB and PC be its radii.

PA = PB = PC

PA² = PB² = PC²

(x-6)² + (y+6)² = (x-3)² + (y+7)²

x² + 36 - 12x + y² + 36 +12y = x² + 9 - 6x + y² + 49 + 14y

 6x + 2y = 14 -------------(1)

Also, (x-3)² + (y+7)² = (x-3)² + (y-3)²

x² + 9 - 6x + y² + 49 + 14y = x² + 9 -6x + y² - 6y + 9

 20y = -40

Therefore y = -2

Substituting in (1), we get: 6x - 4 = 14

x = 18/3 = 6

So the coordinates of the centre are P(6,-2)