The eccentricities of conic sections with one focus at the origin and the directrix corresponding and sketch a graph:displaystyle{e}={2}, directrix displaystyle{r}=-{2} sec{theta}.

Alyce Wilkinson 2021-03-09 Answered

The eccentricities of conic sections with one focus at the origin and the directrix corresponding and sketch a graph:
e=2,
r=2secθ.

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Expert Answer

Neelam Wainwright
Answered 2021-03-10 Author has 102 answers
e=2,r=2secθ
Since e>1, therefore the conic is a hyperbola.
Now consider the directrix,
r=2secθ
r=2cosθ
rcosθ=2
x=2
Now comparing whith x=p, we get
p=2
Therefore equation is,
r=ep1ecosθ
r=2212cosθ
r=412cosθ
Now the graph is,
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