Answer:
(- 4, - 8 ), radius = 7
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 + 8x - 16y + 31 = 0
Collect the x- terms, collect the y- terms together and subtract 31 from both sides.
x² + 8x + y² - 16y = - 31
Use the method of completing the square on the x and y terms
add ( half the coefficient of the x/ y term )² to both sides
x² + 2(4)x + 16 + y² + 2(- 8)y + 64 = - 31 + 16 + 64
(x + 4)² + (y - 8)² = 49 ← in standard form
with centre = (- 4, 8 ) and r = [tex]\sqrt{49}[/tex] = 7
