Answer:
centre = (- 4, 8 ) , radius = 12
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 abd r is the radius
given
x² + 8x + y² - 16y - 64 = 0 ( add 64 to both sides )
x² + 8x + y² - 16y = 64
using the method of completing the square
add ( half the coefficient of the x and y terms)² to both sides
x² + 2(4)x + 16 + y² + 2(- 8)y + 64 = 64 + 16 + 64
(x + 4)² + (y - 8)² = 144 ← in standard form
with centre (- 4, 8 ) and r = [tex]\sqrt{144}[/tex] = 12
