Answer:
(3, - 4 ), r = 9
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 - 6x = 56 - 8y ( add 8y to both sides )
x² + y² - 6x + 8y = 56 ( collect x and y terms together )
x² - 6x + y² + 8y = 56
Use the method of completing the square
add ( half the coefficient of the x/y term )² to both sides
x² + 2(- 3)x + 9 + y² + 2(4)y + 16 = 56 + 9 + 16
(x - 3)² + (y + 4)² = 81 ← in standard form
with centre = (3, - 4 ) and r =
= 9