A conic section with a focus at the origin, with eccentricity [math]e[/math], and with a vertical directrix [math]k[/math] units to the right of the origin has this polar equation:[br] [math]r=\frac{ek}{1+e\cos\theta}[/math] [br]This single equation works for all three conic sections: ellipses when [math]e<1[/math], parabolas when [math]e=1[/math], and hyperbolas when [math]e>1[/math].

[i]This applet was developed for use with [url=https://www.pearson.com/en-us/subject-catalog/p/interactive-calculus-early-transcendentals-single-variable/P200000009666]Interactive Calculus[/url], published by Pearson.[/i]