Parametric curve between two points

[ct.rhino (CT)]

Yes, I am trying to do something like this

Transform curve with graph mapper keeping end points?

Hi, I believe this is a quick one, but I can’t figure it out, suppose I have a 45 degree curve from 0,0,0. And I want to control its curvature with a conic graph mapper, but keeping the start and end points. Like so: [Curve]