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Math Help - Help with parameterizing

  1. #1
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    Help with parameterizing

    Can someone give me direction on where to begin with parameterizing the function of f(x,y) = x^2+y^2-x-y. I know that x = r cos t, y = sin t and r = z. the shape of this function is a paraboloid. I believe that the function in the x-y planes would be a circle. that being said, I think I can say (cos t, sin t, ?t^2?). Any help or direction would be greatful.
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  2. #2
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    (x-1/2)^2 - 1/4 + (y-1/2)^2 - 1/4=f(x,y)

    (x-1/2)^2 +(y-1/2)^2 =f(x,y)+1/2

    (x-1/2)^2 +(y-1/2)^2 =\sqrt{f(x,y)+1/2}^2

    You can see the cross sections are circles which are centered in (1/2,1/2).

    Why you need to parametrize it?

    If you want to parametrize the equations would be:

    x=t, y=s, z=(t-1/2)^2 +(z-1/2)^2 - 1/2
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  3. #3
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    Thanks for the help.

    I am trying to find the max and min on an interval. I did some additional reading and found out that all I need to do is sub. X= cos t and y = sin t. From here I find the derivative, which is 2(sin t cos t - sin t cos t) + cos t - sin t = cos t - sin t. This is were I am at. I have to do some more studying before I can complete the problem.

    My intial thought of find the param. was incorrect, but your insight was verry helpful.
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