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Chapter 11: Problem 19

Find a parametric representation of the surface. The portion of \(z=4-x^{2}-y^{2}\) above the \(x y\) -plane

Short Answer

Expert verified
The parametric representation of the surface is \((x, y, 4-x^2-y^2)\).

Step by step solution

01

Identifying parameters

It can be observed that the variables \(x\) and \(y\) can be chosen as the parameters. This is because they appear independently in the equation.
02

Constructing the parametric representation

Let \(x = x\) and \(y = y\) be parameters. Then the equation can be explained as, \(z = 4 - x^{2} - y^{2}\). So the parametric representation of the surface is \((x, y, 4-x^{2}-y^{2})\). This represents any point on the surface above the xy-plane.

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Most popular questions from this chapter

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