Try to sketch by hand the curve of intersection of the parabolic cylinder and the top…

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Try to sketch by hand the curve of intersection of the parabolic cylinder

y = x^2

and the top half of the ellipsoid

x^2 + 4y^2 + 4z^2 = 16

. Then find parametric equations for this curve and use these equations and a computer to graph the curve.