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Home » Let \(x\) be the width of the path. - Groen Casting

Let \(x\) be the width of the path. - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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First, separate the \( x \) and \( y \) terms:
Complete the square for the \( x \)-terms:
9(x^2 - 4x) = 9((x-2)^2 - 4) = 9(x-2)^2 - 36
Complete the square for the \( y \)-terms:
4(y^2 + 4y) = 4((y+2)^2 - 4) = 4(y+2)^2 - 16
Substitute these back into the equation:
9(x-2)^2 - 36 + 4(y+2)^2 - 16 = -36
9(x-2)^2 + 4(y+2)^2 - 52 = -36
Add 52 to both sides:
9(x-2)^2 + 4(y+2)^2 = 16

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