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Home » Check if this point lies within the circular region: - Midis

Check if this point lies within the circular region: - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 ight)^2}{rac{64}{9}} = 1.

📌 Note that $ rac{64}{3} = rac{192}{9} > rac{64}{9} $, so the $ z $-axis term has larger denominator â but $ x^2 $ and $ \left(z + rac{4}{3}

📌 ight)^2 $ term has same denominator $ rac{64}{9} $, and $ y^2 $ has $ rac{192}{9} $, so it's **elliptical** in $ x/z $-plane. But more precisely, since the equation resembles $ rac{x^2 + y^2}{a^2} + rac{(z - z_0)^2}{b^2} = 1 $, with $ a

📌 e b $, this is an **ellipsoid**. But due to symmetry about $ z $-axis (independent of $ heta $), it's a **rotationally symmetric ellipsoid**. However, the original form $

📌 ho = rac{4}{2 + \cos\phi} $ is a **conic in polar form** with fixed $ heta $, so it's a **conic with focus at origin** â standard form $

📌 ho = rac{ed}{1 + e\cos\phi} $ identifies conic type.

📌 ho = rac{4}{2 + \cos\phi} = rac{2}{1 + rac{1}{2}\cos\phi}.

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