Describe the surface giventhe shape ie parabolid by the para

Describe the surface given(the shape i.e. parabolid) by the parametric equations.

x(s,t)=s cos2t, y(s,t)=s² z(s,t)=s sin2t

Please explain how you came to your answer. Thank you.

Solution

r(s,t)=< s* cos (2t) , s^2 , s * sin (2t) >

x = s*cos (2t), y=s², z=s* sin(2t)
x²+z² = s²(cos²(2t)+sin²(2t)) = s² = y

x²+z² = y