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Polar equation of conic section

Updated: 11/3/2022
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The parametric forms are:

Circle: (r cos θ, r sin θ),

Ellipse: (a cos θ, b sin θ),

Parabola: (at^2, 2at),

Hyperbola: (a sec θ, b tan θ) or (±a cosh u, b sinh u),

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Q: Polar equation of conic section
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A conic section is a curve formed by the intersection of a plane with a cone (conical surface). If the section is parallel to the base of the cone, the conic section has a fixed diameter and is a circle. Any other plane that does not intersect the apex is either a parabola, a hyperbola, or an ellipse.


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Conic projections are better for polar regions because they show these areas with less distortion compared to other map projections. Conic projections maintain shape and direction well along the lines of latitude, making them ideal for representing polar regions accurately.


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