# Sketch the surface of a paraboloid

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1. Jan 24, 2017

### CricK0es

1. The problem statement, all variables and given/known data
Sketch the surface of a paraboloid z=9-x2 -92 in 3-dimensional xyz-space

2. Relevant equations

I assume partial derivatives are involved in some manner

3. 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

Last edited by a moderator: Jan 24, 2017
2. Jan 24, 2017

### SammyS

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

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

3. Jan 24, 2017

### Buffu

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

4. Jan 24, 2017

### Staff: Mentor

Do you mean $z = 9 - x^2 - y^2$?
Neither ordinary derivatives nor partial derivatives are required in this problem.
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.

5. Jan 24, 2017

### CricK0es

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