Given this equation of a circle, x2 + y2 + 8x – 4y + 12 = 0. using completing the square, identify the coordinates of the center of the circle. also, give the length of the radius of the circle. include all work for full credit.

x² + y² + 8x - 4y + 12 = 0

Circle equation: (x - a)² + (y - b)² = r², so,

x² - 2.x.a + a² + y² - 2.y.b + b² - r² = 0

x² + y² - 2ax - 2by + a² + b² - r² = 0

-2ax = 8x

-2a = 8

a = 8/-2

a = -4

-2by = -4y

-2b = -4

b = -4/-2

b = 2

So, (x + 4)² + (y - 2)² - r² = 0

a² + b² - r² = 0

(-4)² + 2² = r²

16 + 4 = r²

r² = 20

So, after all:

(x + 4)² + (y - 2)² = 20

The coordinates of the center is always the opposite of a and b,

So, the center is (-4, 2)

And the radius is r² = 20 => r = √20 => r = 2√5

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