Why is the eccentricity of a catenary equal to sqrt(2)?

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I understand that eccentricity defines how circular a conic section is... but a catenary isn't a conic section - so why is its eccentricity equal to that of a rectangular hyperbola: $\sqrt 2$ ? How does it have an eccentricity in the first place? Are there other figures that aren't conics that still has an eccentricity?