Answer:
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
