What is the center this circle?
x2 + y2 + 6x – 10y + 18 = 0

(- 3, 5 )

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 + 6x - 10y + 18 = 0 (collect x terms and y terms together )

x² + 6x + y² - 10y + 18 = 0 ( subtract 18 from both sides )

x² + 6x + y² - 10y = - 18

Use the method of completing the square on both the x and y terms

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

x² + 2(3)x + 9 + y² + 2(- 5)y + 25 = - 18 + 9 + 25, that is

(x + 3)² + (y - 5)² = 16 ← in standard form

with centre = (- 3, 5 ) and r = = 4

Step-by-step explanation:

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