Give the eccentricities of conic sections with one focus at

Clifland

Clifland

Answered question

2021-08-14

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

Answer & Explanation

Talisha

Talisha

Skilled2021-08-15Added 93 answers

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=ke1ecosθ
Obtain the polar equation as follows.
e=14 and k=2
r=2×14114cosθ=124cosθ4
 r=24cosθ
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=ke1esinθ
Obtain the polar equation as follows.
e=13 and k=6
r=6×13113sinθ=23sinθ3
 r=63sinθ

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?