Answer:
radius: 9
center: (-6, -8)
Explanation:
First, you may wan to rearrange the equation so it is easier to sole, like:
x^2 + 12x + y^2 + 16y + 19 =0
Next, we need to complete the square. x^2 + 12x is the start of the square of x + 6, which ends in 36, and y^2 + 16y is the start of the square of x + 8, which ends in 64. We can start to write in the squares like:
x^2 + 12x + 36 - 36 + y^2 + 16y + 64 - 64 + 19 = 0
(36 & 64 are subtracted so the equation stays the same)
You can factor getting:
(x + 6)^2 - 36 + (y + 8)^2 - 64 + 19 = 0
You can combine the constants to get -36 - 64 + 19 = -81 and we can add 81 to both sides to get:
(x + 6)^2 + (y + 8)^2 = 81
The standard form of a circle equation is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center and r is the radius.
In this case, by substituting, we get the center is (-6, -8) and the radius is 9.