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

Ellipse
Explanation:
The polar equation of a conic, referred to a/the focus as the pole ${\displaystyle r=0}$ and the perpendicular from the pole to the (corresponding)
directrix as the initial line ${\displaystyle \theta =0}$, is
${\displaystyle \frac{l}{r}=1+e\cos \theta }$, where
e is the eccentricity of the conic and l is the semi latus rectum = #
${\displaystyle \left(\frac{1}{2}\right)}$ 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 #
${\displaystyle e<=>1.}$#
Interestingly, for the circle the focus is at the center and ${\displaystyle l=}$ radius a and ${\displaystyle e=0}$. The equation is simply ${\displaystyle r=a}$.
Here, the equation is
${\displaystyle \frac{3}{r}=1+\frac{1}{2}\cos \theta }$. So, ${\displaystyle e=\frac{1}{2}<1}$, and so, the conic is an ellipse. The semi major axis a is given by
${\displaystyle l=a(1-e^2)=a(1-\frac{1}{4})=3\frac{a}{4}=3}$. So, ${\displaystyle a=\frac{1}{4}}$.