tell the center and radius of the circle for this equation

Question

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

Answer 1

To transform the equation into center-radius form the idea is to complete the square for two binomials, one for x and another for y.

x² + 6x + ____ + y² + 4y + _____ = -4

What numbers go in the blanks to complete the square. Since the leading coefficients of the squared terms are one, all that is necessary is to take 1/2 of "b" and square the result.

1/2 of 6 = 3 and 3²=9

1/2 of 4 = 2 and 2²=4

x² + 6x + 9 + y² + 4y + 4 = -4 + 9 + 4 (had to add 9 and 4 to both sides to keep equation in balance)

Now write the trinomials as binomials squared (that was the point for completing the square).

(x + 3)² + (y + 2)² = 9

The center is at (-3, -2) and the radius is 3 (since 3²=9).

desmos.com/calculator/kqvlihny9w

Visit the above graph and use the slider on x_1 to see that the radius is always 3.