Jawab:

a. (x + 1)² + (y - 3)² = 16

b. 4 satuan

c. x = -5

Penjelasan dengan langkah-langkah:

x² + y² + Ax + By + C = 0

(-1, 7) → (-1)² + 7² - A + 7B + C = 0

-A + 7B + C = -50

x² + y² + Ax + By + C = 0

(-5, 3) → (-5)² + 3² - 5A + 3B + C = 0

-5A + 3B + C = -34

x² + y² + Ax + By + C = 0

(-1, -1) → (-1)² + (-1)² - A - B + C = 0

-A - B + C = -2

-A + 7B + C = -50

-5A + 3B + C = -34

______________

4A + 4B = -16

A + B = -4

-5A + 3B + C = -34

-A - B + C = -2

______________

-4A + 4B = -32

A - B = 8

A - B = 8

A + B = -4

_______

-2B = 12

B = -6

A + B = -4

A - 6 = -4 → A = 2

-A - B + C = -2

-2 + 6 + C = -2 → C = -6

a. Persamaan lingkaran nya

x² + y² + 2x - 6y - 6 = 0

b. Ubah ke bentuk standar

x² + 2x + 1 + y² - 6y + 9 = 6 + 1 + 9

(x + 1)² + (y - 3)² = 16

r² = 16 → r = 4

c. Persamaan garia singgung di titik B(-5, 3)

(x₁ - a)(x - a) + (y₁ - b)(y - b) = r²

(-5 + 1)(x + 1) + (3 - 3)(y - 3) = 16

-4x - 4 = 16

x + 1 = -4

x = -5