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How do you fully define a spline?

Hi! I am trying to approximate an involute curve by connecting the end of these lines with a spline. However, the points on the end of the spline are being reported as "loose ends", and I am not sure how to fully define the spline with the necessary constraints. Originally, I speculated it was because I had not constrained the control points, but fixing that also did not seem to address the issue. Do you know what I might be missing here? Is a spline the right tool for this job? Really appreciate the help!
Answers
have you defined the magnitude of the spline ends? see the little white circles near the ends.
I see red spots on the ends of the spline, This is because the direction/magnitude handles are not set. If you tug on them the spline will change. You'll have to calculate this position some how.