At what points does the curve intersect the paraboloid ?

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

At what points does the curve r(t)=ti+(2t−t2)k\mathbf{r}(t) = t \mathbf{i} + (2t - t^2) \mathbf{k} intersect the paraboloid z=x2+y2z = x^2 + y^2 ?

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