Question

Find the centre of a circle passing through points (6, 2), (-1, 3) and (-3, -1).

Answer 1

given,

A(6,2) B(-1,3) C(-3,-1)
_________
OA = √(x-6)²+(y-2)²
________
OB = √(x+1)²+(y-3)²
_________
OC = √(x+3)²+(y+1)²

let O(x,y) be the centre of the circle.

OA=OB ( raddi of same circle )
_________ _________
=>√(x-6)²+(y-2)² = √(x+1)²+(y-3)²

squaring on both sides

=>(x-6)²+(y-2)² = (x+1)²+(y-3)²

=>x²+36-12x+y²+4-4y = x²+1+2x+y²+9-6y

=>36-12x+4-4y-1-2x-9+6y = 0

=>30-14x+2y = 0

=>30 = 14x-2y

=>7x-y = 15..............(1)

OA=OC
_________ _________
=>√(x-6)²+(y-2)² = √(x+3)²+(y+1)²

squaring on both sides

=>(x-6)²+(y-2)² = (x+3)²+(y+1)²

=>x²+36-12x+y²+4-4y = x²+9+6x+y²+1+2y

=>36-12x+4-4y-9-6x-1-2y = 0

=>30-18x-6y = 0

=>30 = 18x+6y

=>5 = 3x+y..............(2)

Add (1) and (2)

=>7x-y+3x+y = 15+5

=>10x = 20

=>x = 20/10 = 2

substitute x=2 in (2)

3x+y=5

=>3(2)+y = 5

=>y = 5-6 = -1

The center of the circle is (2,-1)

HOPE U UNDERSTAND

PLS MARK IT AS BRAINLIEST

Answer 2

please go through the attachment for steps ^-^

the answer is (2,-1)