Equation of a curve between two points whereas the curve limits are defined by the two points

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I've been trying to find a way in python to calculate an equation of a curved line that intersects the axis of their respective points at exactly 90 degrees whereas the curve does not exceed the y-value of the first point and the x-value of the second point. As a visual, I'm trying to write some code that creates an equation for a line like this one:

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Is there anyway that something like this would be possible? Thank you!

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