The parametric representation r(s,t)=2tcos(s)i + 2tsin(s)j + tk for s∈R and t∈R corresponds to what surface?
For this question, is it starts with x=2tcos(s), y=2tsin(s),z=t? what are the next steps?

Question

The parametric representation r(s,t)=2tcos(s)i + 2tsin(s)j + tk for s∈R and t∈R corresponds to what surface? 
For this question, is it starts with x=2tcos(s), y=2tsin(s),z=t? what are the next steps?

anonymous · Answer

x^2 + y^2 = 4t^2[cos^2 (s) + sin^2 (s)] = 4t^2 = 4z^2

So the Cartesian equation for the surface is  z^2 = (1/4)[x^2 + y^2]. So it is a cone