$$\text { Consider the polar equation } r = - \frac { 13 } { 4 \sin \theta - 1 } \text {. }$$

Essay

$$\text { Consider the polar equation } r = - \frac { 13 } { 4 \sin \theta - 1 } \text {. }$$ (a) Find the eccentricity and an equation of the directrix of the conic.
(b) Identify the conic.
(c) Sketch the curve.