Answer:
(10, - 4 ), r = 1
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 the radius
Given
x² + y² - 20x + 8y + 115 = 0
Collect the x- terms and collect the y- terms and subtract 115 from both sides.
x² - 20x + y² + 8y = - 115
Complete the square on both the x and y terms
add ( half the coefficient of the x/ y term )² to both sides
x² + 2(- 10)x + 100 + y² + 2(4)y + 16 = - 115 + 100 + 16
(x - 10)² + (y + 4)² = 1 ← in standard form
with centre = (10, - 4 ) and radius = 1