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Math Help - Is this a cone or an ellipsoid?

  1. #1
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    Is this a cone or an ellipsoid?

    I'm having some trouble figuring out if the equation z = 2 - sqrt(x^2 + y^2) is a cone, ellipsoid, or something else. If I simplify it to look like one of the forms by professor gave me, I get x^2 + y^2 - (2-z)^2 = 0, which looks like the cone formula. But if I go further it becomes ((x^2)/4) + ((y^2)/4) + ((z^2)/4) - (z/4) = 1, which makes it look like a kind of ellipsoid. Any help would be greatly appreciated and thank you in advance!
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  2. #2
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    As well as comparing the shapes of the formulae you can try interpreting the equation visually. You can see the apex is at (0,0,2) (can you? I mean, you'll minimize the subtracted sqrt expression only by setting x and y to zero). Also, you can see that z is zero where x^2 + y^2 = 2^2... Also, over the x-axis, where y = 0, you have a straight line: z = 2 - x...
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  3. #3
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    Ah, thank you Tom! I'm horrible at graphing equations, hopefully I can remember things like this for the test =p
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