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. 1) e=14, x=−2 2) e=13, y=6

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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.  1) e=14, x=−2  2) e=13, y=6

Talisha · Accepted Answer

Step 1  Problem 1:  Recall the following fact.  Equation of conic with eccentricity e and x=−k corresponding to focus at origin is given by r=ke1−ecos⁡θ  Obtain the polar equation as follows.  e=14 and k=2  r=2×141−14cos⁡θ=124−cos⁡θ4  ⇒ r=24−cos⁡θ  Step 2  Problem 2:   Recall the following fact.  Equation of conic with eccentricity e and y=−k corresponding to focus at origin is given by r=ke1−esin⁡θ  Obtain the polar equation as follows.  e=13 and k=−6  r=−6×131−13sin⁡θ=−23−sin⁡θ3  ⇒ r=−63−sin⁡θ

Give the eccentricities of conic sections with one focus at

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