Question:
The focus of the curve \( y^2 + 4x - 6y + 13 = 0 \) is:
The focus of the curve \( y^2 + 4x - 6y + 13 = 0 \) is:
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For parabolas, completing the square can help in finding the vertex and focus.
Updated On: Jan 12, 2026
- \( (2, 3) \)
- \( (-2, 3) \)
- \( (2, -3) \)
- \( (-2, -3) \)
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The Correct Option is A
Solution and Explanation
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: \[ \boxed{(2, 3)} \]
Final Answer: \[ \boxed{(2, 3)} \]
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