Question

Describe the surface. z = 6 − y2 cone ellipsoid hyperboloid elliptic cylinder hyperbolic cylinder parabolic cylinder elliptic paraboloid hyperbolic paraboloid

Answer 1

The equation z = 6 - y^2 represents a parabolic cylinder because it describes a cylindrical shape where the z-coordinate varies in a parabolic relationship to the y-coordinate, independent of x.

Step-by-step explanation:

The given equation z = 6 - y2 represents a surface where z varies as a function of y only, and x can take any value without changing the surface.

This implies that for each value of y, there is a corresponding value of z and x is unrestricted. This creates lines parallel to the x-axis for each y and z coordinate, forming a cylindrical shape.

However, since z is dependent on y in a quadratic form and there i

s no x dependency, this surface is not a standard cylinder, but instead a type of cylinder called a parabolic cylinder. The fact that z decreases as y increases, in a squared relationship, without depending on x makes it clearly parabolic in nature.

Answer 2

The equation
`z = 6 - y^2` doesn't include variable x, so the equation represents some type of cylinders.

Since
`z=y^2` is equation of parabola, then this is parabolic cylinder (see attached diagrams for details).

Answer: parabolic cylinder