Question

Complete the square to rewrite the following equation. Identify the center and radius of the circle.

x^2 + 4x + y^2 − 6y = −4

Answer 1

\[(x^2 + 4x) + (y^2 - 6y) = -4 \\ (\frac{4}{2})^2 = 2 \\ (\frac{-6}{2})^2 = 9 \\ (x^2 + 4x + 4)+(y^2-6y+9) = -4+4+9 \\ (x^2+4x+4) + (y^2-6y+9)=9\] From there, you can write out the left hand side to something squared plus something squared \[(x-h)^2 + (y-k)^2 = r^2\] where r is radius, and (h,k) is the center