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Math Help - Help with level curve!

  1. #1
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    Help with level curve!

    Hi.

    I want to draw the level curve for the following function.

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

    so if i set c = [x-y^2]/[x^2+y], how can I solve for y? Basically i need y in terms of c and x so I can draw them do i not?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Help with level curve!

    Quote Originally Posted by Kuma View Post
    Hi.I want to draw the level curve for the following function. f(x,y) = [x-y^2]/[x^2+y]
    I don't know the context of the problem and perhaps you only need to draw the zero level curve. In that case

    \frac{x-y^2}{x^2+y}=0\Leftrightarrow (x-y^2=0)\;\wedge (x^2+y\neq 0)

    That is, the parabola x=y^2 excluding the points (0,0),\;(1,-1) .
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    Re: Help with level curve!

    Yes at the point 0 I will get a parabola, but I want to draw the level curves for more than 1 point. Suppose c=-2 and c=2, what can i do then?
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    MHF Contributor FernandoRevilla's Avatar
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    Re: Help with level curve!

    Quote Originally Posted by Kuma View Post
    Yes at the point 0 I will get a parabola, but I want to draw the level curves for more than 1 point. Suppose c=-2 and c=2, what can i do then?
    Is it out of curiosity? You can use the Newton-Cramer method, but I guess you haven't covered it.
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    Re: Help with level curve!

    Quote Originally Posted by FernandoRevilla View Post
    Is it out of curiosity? You can use the Newton-Cramer method, but I guess you haven't covered it.
    Well it is a question and it asks me to draw more than one level curve, and I would also like to know how to do them because this is a weak point of mine. So basically the only other way to draw these is using the newton cramer method?
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    Re: Help with level curve!

    Quote Originally Posted by Kuma View Post
    Hi.

    I want to draw the level curve for the following function.

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

    so if i set c = [x-y^2]/[x^2+y], how can I solve for y? Basically i need y in terms of c and x so I can draw them do i not?
    cx^2 + cy = x - y^2 \Rightarrow cx^2 + x + y^2 + cy = 0.

    Complete the square in x and y terms and consider what the resulting relation defines for suitable values of c.
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  7. #7
    MHF Contributor FernandoRevilla's Avatar
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    Re: Help with level curve!

    I feel stupid!. A simple conic!
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