Polar Equation of Conic

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

1. Polar equation of conic is

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

 

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

 

2. Angle between two curve 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