Using the following equation, find the center and radius: x² - 4x + y² + 8y = -4

Solution:

Equation of the circle is given by x² + y² + 2gx + 2fy + c = 0 -------(1)

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

Radius of the circle = √(g² + f² - c)

Given, x² - 4x + y² + 8y = -4

x² - 4x + y² + 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.

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Using the following equation, find the center and radius: x² - 4x + y² + 8y = -4

Summary:

Using the following equation, the center and radius of x² - 4x + y² + 8y = -4 is (2, -4) and 4.