Find the eccentricity, b. identify the conic, c. give an equation of the directrix, and d. sketch the conic. r=12/3--10 Cosθ

a) 10/3  

b) hyperbola

c) x = ± 6/5

Step-by-step explanation:

a) A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:

Given the conic equation:

We have to make it to be in the form :

Comparing with  

e = 10/3 = 3.3333, p = 6/5

b) since the eccentricity = 3.33 > 1, it is a hyperbola

c) The equation of the directrix is x = ±p = ± 6/5

b

step-by-step explanation:

a

b

d

step-by-step explanation: