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Math Help - Level Curves question

  1. #1
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    Level Curves question

    I have a question asking me to describe the level curves for the following functions f(x,y) = x^2 + 2y^2 - 3x= 0

    and

    f(x,y) = -6

    How do I go about doing this, for the second case, would the level curve be just a line or an empty set?
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  2. #2
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    Quote Originally Posted by Penguin91 View Post
    I have a question asking me to describe the level curves for the following functions f(x,y) = x^2 + 2y^2 - 3x= 0

    and

    f(x,y) = -6

    How do I go about doing this, for the second case, would the level curve be just a line or an empty set?
    The level curves are the sets where the functions values are constant.


    So for the first one set

    f(x,y)=c \iff x^2+2y^2-3x=c

    Now complete the square on the x terms to get

    \left(x-\frac{3}{2} \right)^2+2y=c+\frac{9}{2}

    \left(x-\frac{3}{2} \right)^2+2y=\frac{2c+9}{2}

    \frac{\left(x-\frac{3}{2} \right)^2}{\frac{2}{2c+9}}+\frac{y}{2c+9}=1

    This is a familiy of ellipses.

    For the 2nd one think of the definition. Where is the function constant
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    Thanks for your reply, that made more sense!
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