Answer:
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)[tex]5y^{2}+2z^{2} = 2 [/tex]
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)[tex]y = -2x^{2} - 2 [/tex]
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 [tex]y = -2x^ 2 - 2[/tex]) . 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)[tex]5x^{2}+2y^{2}+4z^{2} = 5 [/tex]
this is ellipsoid
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1[/tex]
d)4x^(2)-4y^(2)+4z^(2) = 2
hyperboloid
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1[/tex]
{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
