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embassy suites by hilton convention center las vegas - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 4(x^2 - 8x) - 9(y^2 - 6y) = -115.

📌 Complete the square for $ x $: $ x^2 - 8x = (x - 4)^2 - 16 $.

📌 For $ y $: $ y^2 - 6y = (y - 3)^2 - 9 $.

📌 4[(x - 4)^2 - 16] - 9[(y - 3)^2 - 9] = -115 \implies 4(x - 4)^2 - 64 - 9(y - 3)^2 + 81 = -115.

📌 4(x - 4)^2 - 9(y - 3)^2 + 17 = -115 \implies 4(x - 4)^2 - 9(y - 3)^2 = -132.

📌 Divide by $ -132 $ to standardize:

📌 \frac{(y - 3)^2}{\frac{132}{9}} - \frac{(x - 4)^2}{\frac{132}{4}} = 1.

📌 The center is at $ (h, k) = (4, 3) $.

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