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 \[\tan {\phi _1}\tan {\phi _2} = – 1\]