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

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24