X2 + y2 - 20x + 8y + 115 = 0

What is the center of this circle?

What is the radius of this circle?

(10, - 4), r = 1

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 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