Parametrize the curve obtained by intersecting the cylinder x + z 4 and the plane y...

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Parametrize the curve obtained by intersecting the cylinder x² + z² 4 and the plane y = x. Make a single sketch showing both surfaces and their curve of intersection. Finally, find an equation of a second cylinder on which this curve lies. = Show that the curve with parametrization x = t sin 2t, y = t cos 2t, z = t for π/2 ≤ t ≤ 2π lies on the cone z = √x² + y². Sketch the cone and the curve. Parametrize the curve obtained by intersecting the cylinder x² + z² 4 and the plane y = x. Make a single sketch showing both surfaces and their curve of intersection. Finally, find an equation of a second cylinder on which this curve lies. = Show that the curve with parametrization x = t sin 2t, y = t cos 2t, z = t for π/2 ≤ t ≤ 2π lies on the cone z = √x² + y². Sketch the cone and the curve.