$\"\"$

From the given data :

Conic is hyperbola,

Eccentricity is $\"\"$ , and

Directrix is $\"\"$ .

The directrix is vertical and left of the pole.So we can choose the equation is $\"\"$ .

$\"\"$

The eccentricity of a hyperbola is $\"\"$ and the distance between the pole and the directrix is p = 1.

$\"\"$ (Substitute the values : $\"\"$ and p = 1)

$\"\"$

$\"\"$ (Simplify) $\"\"$

The polar equation is $\"\"$ .