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# Using the following equation, find the center and radius: x^{2} - 4x + y^{2} + 8y = -4

**Solution:**

Equation of the circle is given by x^{2} + y^{2} + 2gx + 2fy + c = 0 -------(1)

Centre of the circle = (-g, -f)

Radius of the circle = √(g^{2} + f^{2} - c)

Given, x^{2} - 4x + y^{2} + 8y = -4

x^{2} - 4x + y^{2} + 8y + 4 = 0--------(2)

Comparing (1) and (2)

c = 4

2g = -4

g = -2

2f = 8

f = 4

Centre of the circle = (-(-2), -4) = (2,-4)

Radius = √[(-2)^{2} + (4)^{2} - 4]

= √(4 + 16 -4)

= √16

= 4

Therefore, the centre and radius of the circle is (2, -4) and 4.

## Using the following equation, find the center and radius: x^{2} - 4x + y^{2} + 8y = -4

**Summary:**

Using the following equation, the center and radius of x^{2} - 4x + y^{2} + 8y = -4 is (2, -4) and 4.

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