Absolute extremum a curve

Hi guys
I’ve drawn some curves with Catenary component in grasshopper with several points as theirs input, now I wonder how can I change each Catenary length input to have these curves with the same value of curve’s extremum? ( same Z parameter of middle Point of each Curve )

Something like this is what you want?

CatenarySameHeight_re.gh (11.2 KB)

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I really appreciate @HS_Kim for your favor
it was so practical, but I have a problem for adapting to my work, it seems need your guide again, thank you in advance.

CatenarySameHeight_re.gh (9.6 KB)

CatenarySameHeight_reV2.gh (11.5 KB)


I’m humbled and grateful for all you have done @HS_Kim Your are best.