Determine the center and radius of the following circle equation:
x2 + y2 + 18x – 18y + 113 = 0

centre = (- 9, 9 ), radius = 7

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

x² + y² + 18x - 18y + 113 = 0

Collect the x and y terms together and subtract 113 from both sides

x² + 18x + y² - 18y = - 113

To obtain standard form use the method of completing the square.

add ( half the coefficient of the x/ y term )² to both sides

x² + 2(9)x + 81 + y² + 2(- 9)y + 81 = - 113 + 81 + 81

(x + 9)² + (y - 9)² = 49 ← in standard form

with centre = (- 9, 9 ) and r = = 7

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