Find a polar equation of the conic with focus at the pole and the given eccentricity and directrix.
e=3/2,ysinΘ=1
There is a rule for eccentricity. e > 1 tells you it is what sort of conic? Hint: You're going to need another focus and directrix.
Conics look like this in polar coordinates: $\displaystyle r = \frac{ep}{1\pm e\sin(\theta)}$ parallel to the polar axis, or
$\displaystyle r = \frac{ep}{1\pm e\cos(\theta)}$ perpendicular to the polar axis.
You have e = 3/2 -- Alarm goes off! This is a hyperbola.
If you mean $\displaystyle r\sin(\theta) = 1$, then we have a horizontal line. (Pretty obvious that this tranlsates to y = 1?). Okay, what form is that?
We are so close...
Note: Is that enough information for uniqueness?