In reply to Alain.

Close, but I don't think you want to use "a simple linear regression of Y on X." The indep variable is t, so you want to regress X and Y on t to get the (local) parametric expressions X(t) = b0 + b1*t and Y(t) = c0 + c1*t when t is near t0.

That said, an alternative is to use a parametric cubic spline, which you can compute in SAS by using the SPLINEC and SPLINEV functions in SAS/IML software. The documentation has an example of fitting a planar curve (X(t), Y(t)).