Find the center and the radius of the circle with the equation: x2-4x+y2-12y+31=0

centre = (2, 6) and radius = 3

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

To obtain this form complete the square on both the x and y terms

express the equation as

x² - 4x + y² - 12y = - 31

x² + 2(- 2)x + 4 + y² + 2(- 6)y + 36 = - 31 + 4 + 36

(x - 2)² + (y - 6)² = 9 ← in standard form

with centre = (2, 6) and r = = 3

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step-by-step explanation:

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