Final answer:
The given equation represents a circle with center (-6, -1) and radius √37.
Step-by-step explanation:
The given equation is a quadratic equation in two variables, x and y. It represents a circle when the coefficients of x² and y² are both equal and their sum is non-zero. In this case, the coefficients of x² and y² are both 1, and their sum is 2. Therefore, the equation represents a circle. To find the center and radius of the circle, we need to complete the square for both x and y.
Completing the square for x, we have (x+6)² - 36. Completing the square for y, we have (y+1)² - 1. So, the center of the circle is (-6, -1) and the radius is √(36+1) = √37. Therefore, the equation represents a circle with center (-6, -1) and radius √37.