Answer:
centre = (- 6, - 1 ) , radius = 5
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
Given
x² + y² + 12x + 2y + 12= 0
Collect the x- terms and the y- terms together and subtract 12 from both sides
x² + 12x + y² + 2y = - 12
Using the method of completing the square
add ( half the coefficient of the x / y coefficients )² to both sides
x² + 2(6)x + 36 + y² + 2(1)y + 1 = - 12 + 36 + 1
(x + 6)² + (y + 1)² = 25 ← in standard form
with (h, k ) = - 6, - 1 ) as centre and r = [tex]\sqrt{25}[/tex] = 5
