How do you name the curve given by the conic r=62+sin⁡θ?

Belen Jones

Belen Jones

Answered question


How do you name the curve given by the conic r=62+sinθ?

Answer & Explanation



Beginner2022-02-11Added 13 answers

The polar equation of a conic, referred to a/the focus as the pole r=0 and the perpendicular from the pole to the (corresponding)
directrix as the initial line θ=0, is
lr=1+ecosθ, where
e is the eccentricity of the conic and l is the semi latus rectum = #
(12) X (length of the chord of the conic through the focus,that is perpendicular to the initial line).
The conic is named an ellipse, parabola or hyperbola according as #
Interestingly, for the circle the focus is at the center and l= radius a and e=0. The equation is simply r=a.
Here, the equation is
3r=1+12cosθ. So, e=12<1, and so, the conic is an ellipse. The semi major axis a is given by
l=a(1e2)=a(114)=3a4=3. So, a=14.

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