Find the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² 4 and the half-cone y² = x² + 2z², y ≥ 0. = Example Find a set of parametric equations for the curve of intersection of the x² 1² cylinder + = 1 and the plane y + z = 3. 9 4 Solution. Generating curve of the cylinder: x = 3 cost, y=2 sin t. Since the curve lies on the plane y+z= 3, its z-coordinate must be z=3-y=3-2 sin t. Therefore, a parametrization of the curve of intersection is x = 3 cost, y=2 sint, z=3-2 sin t. x

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