Chapter 13 - Vector Functions - 13.1 Vector Functions and Space Curves - 13.1 Exercises - Page 894: 28

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We are told that the parametric curve $r(t)$ is the intersection of the surfaces $z= x^2$ and $x^2+ y^2 = 1$ We can graph both surfaces and see the intersection. We know that $x^2+ y^2 = 1$ is going to be a cylinder in the $xy$ plane with radius 1. We also know that $z=x^2$ is a curve on the $zx$ plane extending along the $y$ axis.