Find the eccentricity and directrix for the conic with polar

Find the eccentricity and directrix for the conic with polar equation: 20 6+5sin Select one: a, e = 1 and z =- C. e d, e = 6 and y = 4 O

Clearly this is of the form
ed / (1 + esint)

r = 20 / (6 + 5sint)

Divide by 6 :
r = (10/3) / (1 + (5/6)sint)

So, ed = 10/3
e = 5/6

So d = 10/3 * 6/5

d = 60/15

d = 4

Option D

-----------------------------------------------------------------

Option C
r = a * theta

-----------------------------------------------------------------

r = cos(theta)

Converting to rectangular :
r^2 = rcos(t)

x^2 + y^2 = x

x2 - x + y^2 = 0

Add and sub 1/4 :
x^2 - x + 1/4 + y^2 = 1/4

(x - 1/2)^2 + y^2 = 1/4

Center = (1/2 , 0) and radius = 1/2

Option C