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1. Each equation below represents a circle. Place its equation in standard form and then state the coordinates of its center and the length of its radius.
(a) x² + 8x + y2 – 2y = 8
(b) x2 - 6x + y2 - 20 y =12 -
(c) x2 –16x + y2 +10y+88 =
(d) y2 + x2 +8x = 84​

1 Each Equation Below Represents A Circle Place Its Equation In Standard Form And Then State The Coordinates Of Its Center And The Length Of Its Radius A X 8x Y class=

Sagot :

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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