Final answer:
The polar equation of the conic is r = (1/2)(2 - x). To sketch the graph, substitute different values for x into the equation and convert back to Cartesian coordinates.
Step-by-step explanation:
The polar equation of a conic with a focus at the origin, eccentricity e=1/2, and directrix x=2 can be determined using the fact that the eccentricity of a conic is defined as the ratio of the distance between the focus and a point on the conic to the distance between the directrix and the same point. In this case, since the focus is at the origin, the equation becomes: r = (1/2)(2 - x)
To sketch the graph of this conic, you can plot a few points by substituting different values for x into the equation and converting back to Cartesian coordinates.