Which of the following are considered cylinders? hint : try to do this as if it were on the exam. use the traces (or cross-sections) method to draw a picture to you classify. (click all that apply to get credit.)

a. 5y^{2}+2z^{2}=2

b. y=-\left(2x^{2}+2\right)

c. 5x^{2}+2y^{2}+4z^{2} = 5

d. 4x^{2}-4y^{2}+4z^{2} = 2

e. -\left(\cos\! \left(-4y\right)\right)=1-z

f. 2x^{2}+4y^{2}-4z = -1

g. none of the above.

Step-by-step explanation:

A cylinder is a surface that consists of all lines (called rulings) that are parallel to a given line and pass through a given curve in some plane.

a)

this is cylinder , this is ellipse in y-z plane ,but along x-axis ,we shall get the same curve in every possible plane parallel to the yz-plane.

b)

We have to be careful not to draw interpret it as an equation in 2-space even though there is no z - that just means it does not depend upon z. If we sketch this graph in the xy-plane (so z = 0, we obtain the parabola ) . Since there is no z-value in the equation, we shall get the same curve in every possible plane parallel to the x-y-plane. In particular, the graph of this surface will be all vertical lines passing through the curvey = -2x^ 2 - 2 . in the xy-plane. By definition, this makes the graph a cylinder.

C)

this is ellipsoid

d)4x^(2)-4y^(2)+4z^(2) = 2

hyperboloid

{x,y,z can be exchanged to each other}

e)1-z = - cos (-4y)

this is some curve in y-z plane ,so it is cylinder.

f)    

2x^{2}+4y^{2}-4z = -1

elliptical paraboloid

true

step-by-step explanation:

468

step-by-step explanation: