## Related questions with answers

Question

Are the curves $y=(x-C)^{2}$ level curves of a function $f(x, y)$? What property must a family of curves in a region of the xy -plane have to be the family of level curves of a function defined in the region?

Solution

VerifiedAnswered 4 months ago

Answered 4 months ago

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1 of 2Let

$y=(x-C)^{2}.$

The curves of $y$ represents parabola

$y=x^{2},$

which is horizontally shifted for $C$. The curves cannot be level curves of a function $f(x, y)$ defined in $y \geq 0$ because each of these curves intersects all of the others.

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