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# Level Curves watch

1. I have found the domain to be

So the region of the annulus, bounded by two concentric circles, centre the origin with radius 2 and 3.

But for the level curves I have tried letting , but I can't seem to form a nice equation.

The answer says the level curves are concentric circles, but I can't see how.
2. (Original post by NotNotBatman)

I have found the domain to be

So the region of the annulus, bounded by two concentric circles, centre the origin with radius 2 and 3.

But for the level curves I have tried letting , but I can't seem to form a nice equation.

The answer says the level curves are concentric circles, but I can't see how.
Denote then under the root we have hence

So then we just have hence for we have circles center O with radius
3. (Original post by RDKGames)
Denote then under the root we have hence

So then we just have hence for we have circles center O with radius
Thanks; have I made another mistake or should the discriminant be ?
4. (Original post by NotNotBatman)
Thanks; have I made another mistake or should the discriminant be ?
Yeah, forgot to type out the 4 it seems.
5. (Original post by NotNotBatman)

I have found the domain to be

So the region of the annulus, bounded by two concentric circles, centre the origin with radius 2 and 3.

But for the level curves I have tried letting , but I can't seem to form a nice equation.

The answer says the level curves are concentric circles, but I can't see how.
Perhaps worth noting that , where r^2 = x^2 + y^2, and so f(x, y) depends only on r. It's immediate that f(x, y) = k must be a union of circles.
6. (Original post by DFranklin)
Perhaps worth noting that , where r^2 = x^2 + y^2, and so f(x, y) depends only on r. It's immediate that f(x, y) = k must be a union of circles.
Thank you.

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