Determine the center and radius of the following circle equation:
x2 + y2 + 18x – 18y + 113 = 0

centre = (- 9, 9 ), radius = 7

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² + 18x - 18y + 113 = 0

Collect the x and y terms together and subtract 113 from both sides

x² + 18x + y² - 18y = - 113

To obtain standard form use the method of completing the square.

add ( half the coefficient of the x/ y term )² to both sides

x² + 2(9)x + 81 + y² + 2(- 9)y + 81 = - 113 + 81 + 81

(x + 9)² + (y - 9)² = 49 ← in standard form

with centre = (- 9, 9 ) and r = = 7

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

45

step-by-step explanation: