Final answer:
The equation represents a circle with center and radius.
Step-by-step explanation:
The given equation represents a circle in standard form. To find the center and radius, we need to rewrite the equation in the form (x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius.
Using completing the square method, we can rewrite the equation: (x² + 2x) + (y² - 2y) = 47.
Taking half the coefficient of x and y to complete the square, we get (x² + 2x + 1) + (y² - 2y + 1) = 47 + 1 + 1.
Therefore, the equation of the circle is (x + 1)² + (y - 1)² = 49. The center of the circle is (-1, 1) and the radius is the square root of 49, which is 7 units.