Modelling/Plotting curves in 3-D

I have a set of three points in three dimensional space for determining the equation and hopefully plotting a parabolic function. One of the points is the min/max of the parabola while the other two are equidistant from the first point in the y direction. Other than that, the points can be anywhere in a 3D plane.

Is there a way to fit a curve to these three points in 3D? Furthermore, can I plot this curve as just a line, not a surface? Preferably I want to plot this curve into a pre-existing plot that already has several other elements.