Completing the squares, it is found that the center and the radius of the circles are given as follows:
a) The center is (-4,1) and the radius is 5.
b) The center is (3, 10) and the radius is 11.
c) The center is (8,-5) and the radius is 1.
d) The center is (-4,0) and the radius is 10.
What is the equation of a circle?
The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
Item a:
x² + 8x + y² - 2y = 8
Completing the squares:
(x + 4)² + (y - 1)² = 8 + 4² + 1²
(x + 4)² + (y - 1)² = 25
Comparing to the standard equation: The center is (-4,1) and the radius is 5.
Item b:
x² - 6x + y² - 20y = 12
(x - 3)² + (y - 10)² = 12 + 3² + 10²
(x - 3)² + (y - 10)² = 121
The center is (3, 10) and the radius is 11.
Item c:
x² - 16x + y² + 10y + 88 = 0
(x - 8)² + (y + 5)² = -88 + 8² + 5²
(x - 8)² + (y + 5)² = 1
The center is (8,-5) and the radius is 1.
Item d:
x² + 8x + y² = 84
(x + 4)² + (y - 0)² = 84 + 4²
(x + 4)² + (y - 0)² = 100
The center is (-4,0) and the radius is 10.
More can be learned about the equation of a circle at https://brainly.com/question/24307696
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