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📅 July 6, 2026 👤 scraface

Jul 06, 2026

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r^2 - c r + rac{c^2}{4} + z^2 = rac{c^2}{4} \Rightarrow r^2 + z^2 =...
But \(r^2 + z^2 = x^2 + y^2 + z^2\), and \(r = \sqrt{x^2 + y^2}\), so:
Now square both sides carefully:
This is not a sphere â it's a **quartic surface**. But wait: earlier...
Let \(r = \sqrt{x^2 + y^2}\), so:
r^2 + z^2 = c r \Rightarrow r^2 - c r + z^2 = 0
This is a **circular cylinder**? No â it's quadratic. But geometrica...
ho = c \sin\phi\) is a **sphere tangent to the xy-plane** at the origi...
Standard result: In spherical coordinates, \(
ho = 2a \sin\phi\) represents a sphere of radius \(a\) centered at \((...

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