How do you name the curve given by the conic

Dillan Gibbs

Dillan Gibbs

Answered question


How do you name the curve given by the conic r=41+2sinθ?

Answer & Explanation



Beginner2022-02-13Added 12 answers

The polar equation r=l1+ecosθ represents a conic whose eccentricity is e. A focus is the pole and the line from the pole away from the center is the initial line θ=0.
As cosθ=sin(π2θ),
transforming (π2θ)θ.
we get the equation in the given form
This transformation is rotation of the initial line through
π2, about the pole, in the clockwise sense.
For e>1, the conic is named a hyperbola..
Here e=2 and
l=4=a(e21)=3a, and so,
the semi major axis the hyperbola a=43.

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