Below, the line spacing varies from 1/2R to 2R,
so the moirés go from hyperbolas of e = 2, to ellipses of e = 1/2

I am grateful to Erik Max Francis for showing me the concept of conic eccentricity.
 

Check out Xah Lee's Conic section page. He has a lot of information on these beautiful curves.
Look for his explanation of Dandelin spheres, they give insight.
Here is a paragraph on eccentricity Xah wrote:

"A curve such that there is a fixed point F and a fixed line D,
such that for every point P on the curve,
the number distance[P,F]/distance[P,D] is a constant,
then this curve is called a conic section
and can be formed as the intersection of a plane and a double cone.
Likewise, any general intersection of a double cone and a plane
has a point F and line D such that distance[P,F]/distance[P,D] is constant
for any point P on the intersection.
This number distance[P,F]/distance[P,D] is often denoted as 'e',
and is called the eccentricity of the curve conic section."

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