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D. For no $x$ does the statement hold - ECD Germany

📅 May 3, 2026 👤 scraface

May 03, 2026

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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
Divide the entire equation by 16 to get the standard form:
rac{(x-2)^2}{\left(rac{16}{9}
ight)} + rac{(y+2)^2}{4} = 1
This is the equation of an ellipse, as the coefficients of \( (x-2)^2...

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