### Determine the shape and equation of the curve given in a parametric form.

2. A curve C has the parametrization x = a sint cos alpha, y = b sint sin alpha , z = c cost , t â?¥ 0 , where a, b , c, alpha are all positive constants. a) Show that C lies on the ellipsoid x^2/a^2+y^2/b^2+z^2/c^2=1 b) Show that C also lies on a plane that contains the z axis. c) Describe the curve C. Give its equatio