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Polar Equations of Conics Calculator

Online polar conic: ρ=ep/(1−e cosθ) with one focus at the pole.

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ρ=ep/(1−e cosθ)
Type
Focal parameter
Angle

📖 Tutorial | Polar Conic

1. Definition
With one focus at the pole, a conic has ρ=ep/(1−e cosθ); e<1 ellipse, =1 parabola, >1 hyperbola.
2. Formula & Notation
e,pEccentricity, focal parameter
3. Properties & Laws
  • e decides type;
  • θ=0 toward a vertex;
  • Zero denominator undefined;
  • p>0.
4. Steps
  1. Enter e,p,θ;
  2. Click "Find ρ";
  3. Or click "Load Example".
5. Worked Examples
Example: e=0.5,p=6,θ=0: ρ=6.
6. Common Pitfalls
Denominator may vanish;
e=1 parabola;
p is focal parameter.

❓ FAQ | Polar Conic

Equation?
ep/(1−e cosθ).
e?
Type.
θ=0?
Vertex.
Zero denom?
Undefined.
Example?
ρ=6.
Focus?
Pole.