Inserting a tangent curve

Hello Forum.
I’m trying to create a curve between two controllable points.
The curve best suited looks like a ‘Beizer Span’.
Any suggestions on how to use/apply it?
Ultimately, I aim to lathe the curve…to create an adjustable dome-like profile…on the square shape.
Help is most appreciated.
Jason (11.8 KB)

Looks like a BiArc to me. (9.7 KB)

P.S. Here’s how to do it with BzSpan: (10.5 KB)

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Thank you @Joseph_Oster

How do I lathe?
Without being able to find a ‘Lathe’ node…I thought ‘Sweep’ might work…but no joy. (16.7 KB) (15.1 KB)

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Thank you again @Joseph_Oster

I was about to reply by saying that, while I used Negative to get the same Z value in both directions, they can be different values (blue group below)

Then ended up radically simplifying your whole GH model. (9.5 KB)

P.S. If you want that box, I would get it this way (white group): (12.5 KB)

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Once again, great stuff @Joseph_Oster

Hello there @Joseph_Oster
I’m hoping I can reach out again directly.
I can’t work out how to create a fillet radius…and try to get an extruded half-cylinder to blend with the dome shape you help create.
Any pointers or hints would be most welcome. (25.1 KB)