Find the center of the hyperbola represented by the equation 9x² - 4y² + 36x + 8y - 4 = 0.

A (2, -1)

B (-2, 1)

C (1, -2)

D (-1, 2)

✓ Correct Answer: Option B

Group terms and complete the square: 9(x² + 4x) - 4(y² - 2y) = 4. 9(x² + 4x + 4) - 4(y² - 2y + 1) = 4 + 36 - 4. This simplifies to 9(x+2)² - 4(y-1)² = 36. Divide by 36: (x+2)²/4 - (y-1)²/9 = 1. The center is (-2, 1).

💡 Why is B) the correct answer?

The correct answer to the question "Find the center of the hyperbola represented by the equation 9x² - 4y² + 36x + 8y - 4 = 0." is Option B: (-2, 1).

The other options — A) (2, -1), C) (1, -2), D) (-1, 2) — are incorrect for this CLEP Exam Prep question. As explained above: Group terms and complete the square: 9(x² + 4x) - 4(y² - 2y) = 4. 9(x² + 4x + 4) - 4(y² - 2y + 1) = 4 + 36 - 4. This simplifies to 9(x+2)² - 4(y-1)² = 36. Divide by 36: (x+2)²/4 - (y-1)²/9 = 1. The c…

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How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free CLEP Exam Prep practice test or use flashcards for spaced repetition review.

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Find the center of the hyperbola represented by the equation 9x² - 4y² + 36x + 8y - 4 = 0.

✓ Correct Answer: Option B

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