Question 1080588
{{{r = 4/(-2-cos(theta))}}}

{{{r = 4/-2(1+(1/2)cos(theta))}}}

{{{r = -2/(1+(1/2)cos(theta))}}}.....compare to {{{r = ed/(1+(e)cos(theta))}}} and you see that:

{{{ed = -2}}} and {{{e = 1/2}}} and 
{{{(-1/2)d = 2}}}

{{{d = -2/(1/2)}}}

{{{d = -4}}}

Since {{{e < 1}}}, we have the equation of an ellipse. The form of the equation tells us that the directrix is perpendicular to the polar axis and that its Cartesian equation is {{{x = -4}}} which is vertical line.

so, answer is: A.) {{{Vertical}}}