Answer:
The conic is an ellipse ⇒ answer A
Step-by-step explanation:
* Lets explain how to solve the problem
- The polar form equation of a conic with a focus at the origin, the
directrix is y = ± p where p is a positive real number, and the
eccentricity is a positive real number e is r = ep/(1 ± e sin Ф)
# If 0 ≤ e <1, then the conic is an ellipse
# If e = 1, then the conic is a parabola
# If e > 1, then the conic is an hyperbola
- Lets solve the problem
∵ The equation of the conic is r = 3/(4 + 2 sin Ф)
∵ The form of the equation is r = ep/(1 ± e sin Ф)
- We must divide up and down by 4 to make the 1st term of the
denominator equal 1
∴ r = (3/4)/(1 + (2/4) sin Ф)
∴ ep = 3/4
∴ e = 2/4
- Lets use the rules above to identify the type of the conic
∵ e = 2/4 = 1/2
∴ 0 ≤ e < 1
∴ The conic is an ellipse
