Question

Find a parametric representation for the surface. The part of the cylinder y2 + z2 = 121 that lies between the planes x = 0 and x = 2. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of u and/or v.) (where 0 < x < 2)

Answer 1

We can borrow from what we know about cylindrical coordinates to set

$y(u,v)=11\cos u$

$z(u,v)=11\sin u$

where $0\le u\le2\pi$. Then we can let

$x(u,v)=v$

with $0\le v\le2$.

Answer 2

Answer:

y(u,v)=11cosu

z(u,v)=11sinu

where 0≤u≤2$\pi$

therefore x(u,v)=v

we have 0≤v≤2

Step-by-step explanation:

Find a parametric representation for the surface. The part of the cylinder y2 + z2 = 121 that lies between the planes x = 0 and x = 2. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of u and/or v.) (where 0 < x < 2)

thr radius will be square root of 121

r=11

we set cylindrical coordinates to be

horizontal component=rcosu

vertical component=rsinu

y(u,v)=11cosu

z(u,v)=11sinv

where 0≤u≤2$\pi$

therefore x(u,v)=v

we have 0≤v≤2