# Description 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 equation.

https://brainmass.com/math/calculus-and-analysis/description-of-the-curve-given-in-a-parametric-form-413694

#### Solution Preview

We have

x = alpha*sin(t)*cos(alpha)

(1)

y = b*sin(t)*sin(alpha)

(2)

z = c*cos*t (3)

(a) Substituting the values of variables given by the above formulas to the left side of the equation of the ellipsoid and simplifying the obtained expression we obtain sin^2t + cos^2t =1.

This implies that the given curve lies on the given ...

#### Solution Summary

It is determined the shape and the equation of the curve given in a parametric form.