Jawab:

Persamaan umum lingkaran :

(x-a)²+(y-b)² = r²

(2-a)²+(3-b)²=r²...........(1)

(-a)²+(-1-b)²=r²...........(2)

(3-a)²+(-b)² = r² ...........(3)

Jabarkan persamaan (1), (2), dan (3) :

4-4a+a²+9-6b+b²=r² <=> -4a-6b+13 = r²-a²-b²...(4)

a² + 1 + 2b + b² = r² <=> 2b+1 = r²-a²-b²...(5)

9-6a+a²+b² = r² <=> <=> -6a+9 = r²-a²-b²...(6)

-4a-6b+13=2b+1=-6a+9=r²-a²-b²...(7)

2b+1=-6a+9 <=> 6a+2b=8..... (8)

-4a-6b+13=2b+1<=>6a+6b=12....(9)

Eliminasi persamaan (8) dan (9)

-4b = -4 <=> b = 1

Substitusi b ke persamaan (8)

6a+2(1) = 8

6a+2 = 8

6a = 6

a = 1

Cari nilai r dari persamaan (5)

2(1)+1=r²-1-1

3=r²-2

5=r²

Persamaan lingkaran : (x-1)²+(y-1)²=5