SOLUTION: Determine the eccentricity, the type of conic, and the directrix. r = (9)/(5 +6 cos θ)

SOLUTION: Determine the eccentricity, the type of conic, and the directrix. r = (9)/(5 +6 cos θ)

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Question 1140692: Determine the eccentricity, the type of conic, and the directrix.
r = (9)/(5 +6 cos θ)
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

given:

find:
the type of conic
the eccentricity
the directrix:

Standard form for conics in polar equations is

where is the eccentricity, the directrix is = ± if

in your case:
multiply the numerator and denominator by

the eccentricity:

the directrix:
since =>...substitute
=>
=>
=>
so, the directrix is =>

the type of conic:
since , you have

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