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Home » Using the quadratic formula, \(n = \frac{-1 \pm \sqrt1 + 1680}2\). - DNSFLEX

Using the quadratic formula, \(n = \frac{-1 \pm \sqrt1 + 1680}2\). - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 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 geometrically, the surface \(

📌 ho = c \sin\phi\) is a **sphere tangent to the xy-plane** at the origin.

📌 Standard result: In spherical coordinates, \(

📌 ho = 2a \sin\phi\) represents a sphere of radius \(a\) centered at \((0, 0, a)\).

📌 Compare: \(

📌 ho = c \sin\phi = 2 \cdot rac{c}{2} \sin\phi\) â sphere of radius \(rac{c}{2}\), centered at \((0, 0, rac{c}{2})\).

📌 Thus, the shape is a **sphere** of radius \(rac{c}{2}\) centered at \((0, 0, rac{c}{2})\).

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