Table

Table 8: TABLE 8 Polar Equations of Conics (Focus at the Pole, Eccentricity \(e\))

Equation	Description
\(r=\dfrac{ep}{1-e\cos \theta }\)	Directrix is perpendicular to the polar axis a distance \(p\) units to the left of the pole.
\(r=\dfrac{ep}{1+e\cos \theta }\)	Directrix is perpendicular to the polar axis a distance \(p\) units to the right of the pole.
\(r=\dfrac{ep}{1+e\sin \theta }\)	Directrix is parallel to the polar axis a distance \(p\) units above the pole.
\(r=\dfrac{ep}{1-e\sin \theta }\)	Directrix is parallel to the polar axis a distance \(p\) units below the pole.

Eccentricity
If \(e=1,\) the conic is a parabola; the axis of symmetry is perpendicular to the directrix.
If \(e<1,\) the conic is an ellipse; the major axis perpendicular to the directrix.
If \(e>1,\) the conic is a hyperbola; the transverse axis is perpendicular to the directrix.