Answer:
x² + (y + 2)² = 16
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
Given
x² + y² + 4y = 12
Using the method of completing the square
add ( half the coefficient of the y- term)² to y² + 4y
x² + y² + 2(2)y + 4 = 12 + 4
x² + (y + 2)² = 16 ← in standard form
with centre (0, - 2 ) and radius = 4
