(q2) determine the eccentricity, the type of conic, and the directrix for r = 9/1+cos theta

The answer is (d) ⇒ eccentricity = 6 , hyperbola , directrix  x = 3/2

Step-by-step explanation:

∵ r = ek/(1 ± ecosФ)

∵ r = 9/(1 + 6cosФ)

∴ e = 6 ⇒ eccentricity = 6

∵ e > 1

∴ The conic is hyperbola

∵ ek = 9

∴ k = 9/6 = 3/2

∴ The directrix  x = 3/2

452,489 to the nearest thousand is 452,000

d is the correct answer

step-by-step explanation:

x= 8 because 3x = 3 * 8, and 3*8 = 24