For a conic with a focus at the origin, if the directrix is
[tex]y=\pm p[/tex]
where p is a positive real number, and the eccentricity is a positive real number e, the conic has a polar equation
[tex]r=\frac{ep}{1\pm e\sin\theta}[/tex]
if 0 ≤ e < 1 , the conic is an ellipse.
if e = 1 , the conic is a parabola.
if e > 1 , the conic is an hyperbola.
In our problem, our equation is
[tex]r=\frac{5}{1+5\sin\theta}[/tex]
If we compare our equation with the form presented, we have
[tex]\begin{cases}e={5} \\ p={1}\end{cases}[/tex]
Therefore, the directrix is
[tex]y=1[/tex]
