Identify the surface with the given vector equation. r(s,t)=<s\sin2t,s^2,s\cos2t>

smismSitlougsyy

smismSitlougsyy

Answered question

2021-11-16

Identify the surface with the given vector equation.
r(s,t)=<ssin2t,s2,scos2t>

Answer & Explanation

Fearen

Fearen

Beginner2021-11-17Added 15 answers

Once more, we wish to start by writing out the solid's parametric equations. After then, we seek to discover a link between them. We can learn more about the surface thanks to this. This is the equation:
x=ssin2t 
y=s2 
z=scos2t 
Your attention should be instantly drawn to the following:
x2+z2=s2sin22t+s2cos22t=s2=y 
Consequently, the surface is given has the equation:
y=x2+z2 
The y-axis serves as the axis of this paraboloid.

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