Respuesta :
Answer:
The centre is at (-12, 9) and the radius = 5 units.
Step-by-step explanation:
x^2 + y^2 + 24x - 18y + 200 = 0
x^2 + 24x + y^2 - 18y = -200
Completing the square on the x and y terms:
(x + 12)^2 - 144 + (y - 9)^2 - 81 = -200
(x + 12)^2 + (y - 9)^2 = -200 + 144 + 81
(x + 12)^2 + (y - 9)^2 = 25
So the centre is at (-12, 9) and the radius = the square root of 25 = 5.
Answer:
centre = (- 12, 9), radius = 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 + 24x - 18y + 200 = 0
Collect the terms in x/ y together and subtract 200 from both sides
x² + 24x + y² - 18y = - 200
Using the method of completing the square
add ( half the coefficient of the x/ y term )² to both sides
x² + 2(12)x + 144 + y² + 2(- 9)y + 81 = - 200 + 144 + 81
(x + 12)² + (y - 9)² = 25 ← in standard form
with centre (- 12, 9) and r = [tex]\sqrt{25}[/tex] = 5
