Determine e, k, and identify the type of conic for r= 12/ 7- cos theta

The answer is (d) ⇒ e = 1/7 , k = 12 , conic ellipse

Step-by-step explanation:

∵ r = ek/(1 ± ecosФ)

∵ r = 12/(7 - cosФ) ⇒ ÷ 7 up and down

∴ r = 12/7 ÷ 1 - 1/7 (cosФ)

∴ e = 1/7

∵ 12/7 = ke ⇒ 12/7 = k(1/7)

∴ k = 12

∵ 0 < e < 1

∴ The conic is ellipse

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.