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Home » From Heartbreak to Hope: Powerful Mom Quotes Everyone Should Hear Now! - Dachbleche24

From Heartbreak to Hope: Powerful Mom Quotes Everyone Should Hear Now! - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A home-schooled student is studying the properties of conic sections. Determine the type of conic section represented by the equation \( 9x^2 + 4y^2 - 36x + 16y + 36 = 0 \).

📌 To determine the type of conic section, we rewrite the given equation in standard form by completing the square. The equation is:

📌 9x^2 + 4y^2 - 36x + 16y + 36 = 0

📌 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

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