Give the eccentricities of conic sections with one focus at the origin along with the directrix corresponding to that focus. Find a polar equation for each conic section. e = 2, x = 4

Jason Farmer 2021-02-25 Answered
Give the eccentricities of conic sections with one focus at the origin along with the directrix corresponding to that focus. Find a polar equation for each conic section. e=2, x=4
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Expert Answer

Faiza Fuller
Answered 2021-02-26 Author has 108 answers

Step 1

Consider the given: eccentricity, e=2 directrix, x=4 If the eccentricity is greater than 1 then we get a hyperbola. And if the directrix is the line x=d, then we have, r= ed1 + e cos θ

Step 2

According to question: Substitute the value of eccentricity and directrix in polar equation of hyperbola. r= 2(4)1 + 2 cos θ
r= 81 + 2 cos θ

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