Final answer:
The graph of the polar equation 9/(1 - 3sin(theta)) resembles a type of limaçon with a loop, which does not match any of the provided options. It is not a circle, spiral, straight line, or parabola.
Step-by-step explanation:
The question is asking about the graph of the polar equation 9/(1 - 3sin(theta)). To understand the shape this equation will produce when plotted, we examine what happens as the variable theta changes. The denominator 1 - 3sin(theta) suggests that there will be a vertical asymptote whenever sin(theta) equals 1/3, which is where the equation will be undefined. This fact tells us that the graph cannot be a circle, a straight line, or a parabola. The graph of this polar equation forms a shape known as a limaçon, which is a distorted circle that can have an inner loop depending on the coefficients of the sine or cosine terms in the denominator.
However, the specific polar equation given here, 9/(1 - 3sin(theta)), does not fit neatly into any of the general shapes mentioned in the options. Nevertheless, we can determine that it does not represent a circle, spiral, straight line, or a parabolic shape, as these do not match the characteristics of the given equation. Thus, the correct option is not listed among the given choices, and the graph will likely resemble a type of limaçon with a loop, given the presence of the sine function with a coefficient greater than one in the denominator.