Final answer:
The given equation r = 10 / (3 - 2 sin θ) has eccentricity e = 1, indicating that the conic is a parabola.
Step-by-step explanation:
The given equation r = 10 / (3-2 sin θ) represents a conic section. To find the eccentricity and identify the conic, we compare this equation to the general polar form of a conic section r = e / (1 - e cos θ) or r = e / (1 + e sin θ), where e is the eccentricity. If e = 1, the conic is a parabola, if 0 ≤ e < 1, it is an ellipse or a circle (where e = 0), and if e > 1, it is a hyperbola.
In the given equation, rearranging gives us r = 10 / (3 - 2 sin θ) = 1 / ((3/10) - (2/10) sin θ). By comparing the coefficients, we see that the eccentricity e is 1 which means the conic is a parabola.