Answer: The equation of the circle can be rewritten in standard form by completing the square for both x and y terms. The standard form of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
17 + y^2 + 6x = 6y + 63 y^2 - 6y + 6x + 17 = 63 y^2 - 6y + 9 + 6x = 63 + 9 (y - 3)^2 + 6x = 72 (y - 3)^2 + 6(x - (-6)) = 72 (y - 3)^2 + (x + 6)^2 = 72
From this we can see that the center of the circle is (-6,3) and the radius is sqrt(72) = 6sqrt(2).
I’m sorry but I’m unable to draw a graph for you.