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Home » \( \textbase^2 = 100 - 64 = 36 \). - Nurtured Nest

\( \textbase^2 = 100 - 64 = 36 \). - Nurtured Nest

📅 May 8, 2026 👤 scraface

May 08, 2026

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ho = 3c \sin(\phi)\) into \(z =
z = 3c \sin(\phi) \cos(\phi) = rac{3c}{2} \sin(2\phi).
Now express \(
ho^2 = x^2 + y^2 + z^2\):
But \(\sin^2\phi = 1 - \cos^2\phi = 1 - \left(rac{z}{
ight)^2 = 1 - rac{z^2}{x^2 + y^2 + z^2}\). So:
9c^2 \left(1 - rac{z^2}{x^2 + y^2 + z^2}
ight) = x^2 + y^2 + z^2.
Multiply through:
9c^2 - rac{9c^2 z^2}{x^2 + y^2 + z^2} = x^2 + y^2 + z^2.

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