Answer:
(0, - 2 ), r = 6
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 is the radius
Rearrange the given equation collecting the terms in y together, that is
x² + y² + 4y + 4 = 36 ( subtract 4 from both sides )
x² + y² + 4y = 32
Use the method of completing the square on the y- terms
add ( half the coefficient of the y- term)² to both sides
x² + y² + 2(2)y + 4 = 32 + 4
x² + (y + 2)² = 36 ← in standard form
with (h, k ) = (0, - 2 ) and r² = 36, thus
centre = (0, - 2 ) and r = [tex]\sqrt{36}[/tex] = 6
