Final answer:
To find the radius of the circle given by the equation x^2 + 4x + y^2 - 6y = -4, complete the square to rewrite the equation in standard form. The standard form reveals a radius of 3 units.
Step-by-step explanation:
The question provided involves completing the square to find the radius of a circle given by the equation x^2 + 4x + y^2 - 6y = -4. We start by grouping the x terms and the y terms: (x^2 + 4x) + (y^2 - 6y) = -4. Next, complete the square for both x and y by adding and subtracting the square of half the coefficients of the linear terms to both sides of the equation, respectively: x^2 + 4x + 4 - 4 + y^2 - 6y + 9 - 9 = -4.
Simplify to get (x + 2)^2 + (y - 3)^2 = 9. Now, the equation is in the standard form of a circle, (x - h)^2 + (y - k)^2 = r^2, where h and k are the coordinates of the center of the circle, and r is the radius. Comparing the equations gives us a radius r of √9 which is 3.