Answer:
see explanation
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
8x + x² - 2y = 64 - y²
Collect the x/y terms, leaving 64 on the right side, that is
x² + 8x + y² - 2y = 64
To obtain standard form use the method of completing the square.
add ( half the coefficient of the x/y terms )² to both sides
x² + 2(4)x + 16 + y² + 2(- 1)y + 1 = 64 + 16 + 1
(x + 4)² + (y - 1)² = 81 ← in standard form
with centre (- 4, 1) and radius = 9
