Question

Identify the center and radius of each.

x^+y^+24x-18y+200=0

Answer 1

centre = (- 12, 9), radius = 5

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 =
`√(25)` = 5

Answer 2

The centre is at (-12, 9) and the radius = 5 units.

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.