To determine the conic section represented by the given equation, we can analyze the coefficients of the x², y², and xy terms.
The given equation can be rewritten as:
x² + y² - 8x - 10y = -10
Completing the square for x and y, we get:
(x - 4)² - 16 + (y - 5)² - 25 = -10
(x - 4)² + (y - 5)² = 31
Comparing this equation to the standard forms of the conic sections, we can see that it is the equation of a circle with center (4, 5) and radius √31.
Therefore, the answer is (C) Circle