Polar Equation of a Conic

Some important results and formulas regarding the polar equation of a conic are listed here.

1. The polar equation of a conic is

r = \frac{1}{{1 - e\cos \theta }}

  • If e < 1 the conic is an ellipse.
  • If e > 1 the conic is a hyperbola.
  • If e = 1 the conic is a parabola.

2. The angle between two curves is given by

\tan \theta = \frac{{\tan {\phi _1} - \tan {\phi _2}}}{{1 + \tan {\phi _1}\tan {\phi _2}}}

3. Two curves are perpendicular to each other if

\tan {\phi _1}\tan {\phi _2} = - 1