A curve C has the parametrization x = a sint cosα , y = bsint sinα , z = c cost, t ≥ 0
where a, b, c, α 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

I understand how to get a , by replacing the values for x,y,and z, but I am having trouble how to explain b and c

Question

A curve C has the parametrization x = a sint cosα , y = bsint sinα , z = c cost, t ≥  0
where a, b, c, α 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

I understand how to get a , by replacing the values for x,y,and z, but I am having trouble how to explain b and c