Polar Equation of a Conic

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

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