Jawaban:

Penjelasan dengan langkah-langkah:

Persamaan lingkaran:

x² + y² + Ax + By + C = 0

titik A(3, 1)

3² + 1² + 3A + B + C = 0

3A + B + C = -10________(1)

Titik B(-2, 6)

(-2)² + 6² - 2A + 6B + C = 0

-2A + 6B + C = -40_______(2)

Titik C(-5, -3)

(-5)² + (-3)² - 5A - 3B + C = 0

-5A - 3B + C = -34_______(3)

Eliminasi persamaan 1 & 2

3A + B + C = -10

-2A + 6B + C = -40

_______________-

5A - 5B = 30

A - B = 6_________(4)

Eliminasi persamaan 1 & 3

3A + B + C = -10

-5A - 3B + C = -34

_______________-

8A + 4B = 24

2A + B = 6________(5)

Eliminasi persamaan 4 & 5

A - B = 6

2A + B = 6

_________+

3A = 12

A = 4

4 - B = 6

B = -2

3(4) - 2 + C = -10

10 + C = -10

C = -20

Persamaan lingkarannya:

x² + y² + 4x - 2y - 20 = 0