The quartic with implicit equation
The bow has vertical tangents at and horizontal tangents at .
Its curvature is implicitly given by
The area enclosed by the two loops is given by
(OEIS A118321).
The portion of the curve bounding the two loops has approximate perimeter
(OEIS A118322).
More things to try:
Weisstein, Eric W. "Bow." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Bow.html