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does coffee break a fast - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 = x^2 + 2x + 1 + 2x + 2 + 3 = x^2 + 4x + 6.

📌 \(\boxed{x^2 + 4x + 6}\)

📌 Question: A retired engineer is helping design a new exhibit on conic sections. They explore the hyperbola given by \( 9x^2 - 16y^2 = 144 \). Determine the coordinates of its center.

📌 Solution: First, rewrite the equation in standard form:

📌 \frac{9x^2}{144} - \frac{16y^2}{144} = 1.

📌 Simplify the fractions:

📌 \frac{x^2}{16} - \frac{y^2}{9} = 1.

📌 This equation is in the standard form \(\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1\), where \((h, k)\) is the center. Here, \(h = 0\) and \(k = 0\), so the center of the hyperbola is at the origin.

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