Sketch the surface of a paraboloid

[CricK0es]

Homework Statement

Sketch the surface of a paraboloid z=9-x² -9² in 3-dimensional xyz-space

Homework Equations

I assume partial derivatives are involved in some manner

The Attempt at a Solution

[/B]
I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks

 

[SammyS]

Homework Statement

Sketch the surface of a paraboloid z=9-x² -9² in 3-dimensional xyz-space

Homework Equations

I assume partial derivatives are involved in some manner

The Attempt at a Solution

I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks [/B]

Please correct your statement of the problem. It must be in error.

What did you get when you set an individual variable to zero ?

 

[Buffu]

Homework Statement

Sketch the surface of a paraboloid z=9-x² -9² in 3-dimensional xyz-space

Homework Equations

I assume partial derivatives are involved in some manner

The Attempt at a Solution

I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks [/B]

Y-comp is missing, So it can't be 3d shape.

 

[Mark44]

Homework Statement

Sketch the surface of a paraboloid z=9-x² -9² in 3-dimensional xyz-space

Do you mean $z = 9 - x^2 - y^2$?

Homework Equations

I assume partial derivatives are involved in some manner

Neither ordinary derivatives nor partial derivatives are required in this problem.

The Attempt at a Solution

[/B]
I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks

Setting one variable to zero gives you what's called a trace, the intersection of the surface in one of the coordinate planes. For example, assuming the surface is as I wrote it above, setting x = 0, gives you the trace in the y-z plane. Setting y = 0, gives you the trace in the x-z plane.

There are other techniques that can be used. Your textbook should have some examples, especially for paraboloids. These kinds of surfaces have circular cross-sections along some axis.

 

[CricK0es]

Yeah there was a mistake on the question paper, I had to email my tutor, 9² goes to y².

I'll attempt it again with your advice. Thank you

 

[Mark44]

Yeah there was a mistake on the question paper 9² goes to y².

I'll attempt it again with your advice. Thank you

Look for cross sections in a number of planes that are parallel to the x-y plane.