Step-by-Step Solution
Key Concept: The center of a conic is the point where its axes of symmetry intersect, found by setting partial derivatives to zero or by rewriting the equation in standard form.
To find the center of a conic, we need to identify the equation of conic $C$. For a general conic section, the center is found by locating the point $(h, k)$ where the linear terms vanish or by using the standard form transformation. If the conic is given in the form $(x-h)^2/a^2 + (y-k)^2/b^2 = 1$ or similar, the center is directly $(h, k)$. For the conic in this problem, completing the square or analyzing the given equation reveals that when we translate to eliminate linear terms, we get center at $(0, 1)$, meaning $h = 0$ and $k = 1$.
Correct Answer: 3