If the towers are exactly of the same height the minimum distance between ground and conductor is exactly at mid-span and if one tower is higher than another the minimum clearance occours at someplace near the smaller tower. Also please note that towers of different heights can be procured if needed as well as separation between any two towers is not a fixed value.
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The curve is still a catenary. If the lower end is extended, it will rise to the same height as the higher end, and it will form a symmetrical catenary. My calculus book isn't handy, and it has been many years since I reviewed this; but I don't recall it as being too complicated.
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