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Home » Celeb Sounds Collide: Glen Powell and Sydney Sweeney Bridge the Spotlight! - Parker Core Knowledge

Celeb Sounds Collide: Glen Powell and Sydney Sweeney Bridge the Spotlight! - Parker Core Knowledge

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Final answer: $\boxed{2x^4 - 14x^2 + 23}$

📌 Question: A comet follows a hyperbolic trajectory described by $ 4x^2 - 9y^2 - 32x + 54y + 115 = 0 $. Determine the center of the hyperbola.

📌 Solution: Rewrite the equation by completing the square. Group $ x $ and $ y $ terms:

📌 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.

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