Answer:
centre = (- 4, 8 ) , radius = 3
Explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
(h, k ) are the coordinates of the centre and r is the radius
given
x² + 8x + y² - 16y + 71 = 0 ( subtract 71 from both sides )
x² + 8x + y² - 16y = - 71
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 = - 71 + 16 + 64
(x + 4)² + (y - 8)² = 9 , that is
(x - (- 4))² + (y - 8)² = 3² ← in standard form
with centre = (- 4, 8 ) and r = 3