X2 + y2 - 6x + 4y - 12 = 0

y = sqrt (-x^2 + 6 x + 16) - 2 or y = - sqrt (-x^2 + 6 x + 16) - 2

Step-by-step explanation:

Solve for y:

-12 - 6 x + x^2 + 4 y + y^2 = 0

Subtract x^2 - 6 x - 12 from both sides:

y^2 + 4 y = - x^2 + 6 x + 12

Add 4 to both sides:

y^2 + 4 y + 4 = - x^2 + 6 x + 16

Write the left hand side as a square:

(y + 2) ^2 = - x^2 + 6 x + 16

Take the square root of both sides:

y + 2 = sqrt (-x^2 + 6 x + 16) or y + 2 = - sqrt (-x^2 + 6 x + 16)

Subtract 2 from both sides:

y = sqrt (-x^2 + 6 x + 16) - 2 or y + 2 = - sqrt (-x^2 + 6 x + 16)

Subtract 2 from both sides:

Answer: y = sqrt (-x^2 + 6 x + 16) - 2 or y = - sqrt (-x^2 + 6 x + 16) - 2