Question

Find the center and the radius of the circle with the equation:x^2+6x+y^2+4y+12=0

Answer 1

The center is at (-3, -2) and the radius = 1.

Explanation:

We can do this by converting the given equation to standard form.

x^2+6x+y^2+4y+12=0

x^2+6x+y^2+4y = -12

Completing the square on the x and y terms:

(x + 3)^2 - 9 + (y + 2)^2 - 4 = -12

(x + 3)^2 + ( y + 2)^2 = -12 + 9 + 4

(x + 3)^2 + ( y + 2)^2 = 1

So the center is (-3, -2) and the radius = 1.