$\"\"$

The polar equation is $\"\"$ .

Assume its focus is located at the origin.

Its directrix is located at the left at $\"\"$ .

Directrix is perpendicular to the polar axis at a distance $\"\"$ right of the pole.

Let us consider $\"\"$ is a point on the curve.

Consider the following diagram:

$\"\"$

Distance between focus at origin and the point $\"\"$ is $\"\"$ .

Distance between $\"\"$ and directrix is $\"\"$ .

$\"\"$

Definition of eccentricity : $\"\"$ .

$\"\"$

$\"\"$ .

The polar equation of a conic with focus at the pole and directrix perpendicular to

the polar axis distance $\"\"$ right of the pole, then the equation is $\"\"$ .

$\"\"$

The polar equation is $\"\"$ .