Jawab:

Penjelasan dengan langkah-langkah:

x² + y² + ax + by + c = 0

(1, 5), (-2, 4), (5, -3)

1² + 5² + a(1) + b(5) + c = 0

a + 5b + c = -1 - 25

a + 5b + c = -26

(-2)² + 4² + a(-2) + b(4) + c = 0

-2a + 4b + c = 4 - 14

-2a + 4b + c = -10

(5)² + (-3)² + a(5) + b(-3) + c = 0

5a - 3b + c = 9 - 25

5a - 3b + c = -16

a + 5b + c = -26

-2a + 4b + c = -10

5a - 3b + c = -16

a = -26 - 5b - c

-2 (-26 - 5b - c) + 4b + c = -10

52 + 10b + 2c + 4b + c = -10

14b + 3c = -10 - 52

14b + 3c = -62

3c = -62 - 14b

c = (-62/3) - (14/3)b

5a - 3b + c = -16

5(-26 - 5b - c) - 3b + (-62/3) - (14/3)b = -16

-130 - 25b - 5c - 3b - (62/3) - (14/3)b = -16

-130 - 25b - 5((-62/3) - (14/3)b) - 3b - (62/3) - (14/3)b = -16

-130 - 25b + (310/3) + (70/3)b - 3b - (62/3) - (14/3)b = -16

(-25 + (70/3) - 3 - (14/3))b = 130 - (310/3) + (62/3) - 16

(-75 + 70 - 9 - 14)b = 390 - 310 + 62 - 48

-28b = 94

b = -94/28 = - 47/14

c = (-62/3) - (14/3)(-47/14)

c = (-62/3) + (47/3)

c = -15/3

c = -5

a = -26 - 5b - c

a = -26 - 5(-47/14) - (-5)

a = -21 + (239/14)

a = (-294 + 239)/14

a = -55/14

Persamaan lingkaran :

x² + y² + (-55/14)x + (-47/14)y - 5 = 0

14x² + 14y² - 55x - 47y - 70 = 0