Answer
Ellipse
See graph
Work Step by Step
We are given the polar equation:
$r=\dfrac{6}{2-\sin\theta}$
Rewrite the equation:
$r=\dfrac{\dfrac{6}{2}}{\dfrac{2-\sin\theta}{2}}$
$r=\dfrac{3}{1-\dfrac{1}{2}\sin\theta}$
The equation is in the form:
$r=\dfrac{ep}{1-e\sin\theta}$
Determine $e$ using the denominator:
$e=\dfrac{1}{2}$
Determine $p$ using the numerator:
$ep=3$
$\dfrac{1}{2}p=3$
$p=6$
Because $e<1$, the conic is an ellipse. Its directrix is parallel to the polar axis at a distance of 6 units below the pole. The major axis is perpendicular to the directrix.
Graph the curve:
