Final answer:
The eccentricity is 0, and the conic section is a circle.
Step-by-step explanation:
To find the eccentricity and identify the conic, we use the formula
r = \frac{8}{3+3\cos \theta}
The eccentricity (e) of a conic section is defined as the ratio between the distance between the center and a focus of the conic section (c) and the distance between the center and a point on the conic section (r). In this case, the center is at (0,0) and the conic section is in polar coordinates, so we can convert to Cartesian coordinates using
x = r\cos \theta
y = r\sin \theta
Substituting these values into the equation and rearranging, we get
x^2 + \left(y-\frac{4}{3}\right)^2 = \left(\frac{4}{3}\right)^2
This equation represents a circle with a center at (0,4/3) and a radius of 4/3. Therefore, the conic section is a circle and the eccentricity is 0.