Is there a function of two variables whose z = 0 level curve consists exactly of
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Is there a function of two variables whose z = 0 level curve consists exactly of

[From: ] [author: ] [Date: 12-07-12] [Hit: ]
......
the circles x^2 +y^2 =5 and x^2 +y^2 =10? If so, what is an example? If not, why not?

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z = (x^2 + y^2 - 5) (x^2 + y^2 - 10)
at z=0
(x^2 + y^2 - 5) (x^2 + y^2 - 10) = 0
x^2 + y^2 - 5 = 0
x^2 + y^2 - 10 = 0
1
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