Question

The focus of the curve \( y^2 + 4x - 6y + 13 = 0 \) is:

• A. \( (2, 3) \)
• B. \( (-2, 3) \)
• C. \( (2, -3) \)
• D. \( (-2, -3) \)

Hint:

For parabolas, completing the square can help in finding the vertex and focus.

Answer 1

The Correct Option is A

Step 1: Rearranging the equation to the standard form of a parabola: \[ y^2 - 6y = -4x + 13. \] Complete the square for \( y \): \[ (y - 3)^2 = -4(x - 2). \] Step 2: The vertex is at \( (2, 3) \) and the focus is at \( (2, 3) \).

Final Answer: \[ \boxed{(2, 3)} \]