Answer :
Answer:
(- 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 = [tex]\sqrt{16}[/tex] = 4