$\"\"$ \ \

\

The rectangular equation is $\"\"$ .

\

Rewrite the equation: $\"\"$ .

\

The equation is in the form of standard equation of ellipse: $\"\"$ .

\

Here $\"\"$ , $\"\"$ and $\"\"$ .

\

For an ellipse $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

The eccentricity is $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$

\

The eccentricity of ellipse is $\"\"$ .

\

$\"\"$

\

The directrix of horizontal ellipse is $\"\"$ .

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$ .

\

Let $\"\"$ .

\

$\"\"$

\

The directrix is $\"\"$ .

\

If the directrix is a horizontal line $\"\"$ , then the polar equation of the conic is $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

The polar equation is $\"\"$ .

\

$\"\"$

\

The polar equation is $\"\"$ . \ \