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Math Help - Find points on the curve closest to the origin.

  1. #1
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    Find points on the curve closest to the origin.

    Find points on the curve x^2-xy+y^2=9 closest to and farthest from the origin.

    I know the distance of point from the origin is, r = sqrt(x^2 + y^2)

    Then I subbed the equation into, r(x) = sqrt(x^2 + [f(x)]^2)

    and got 9 = sqrt(x^2 + [x^2-xy+y^2]^2)

    and I'd solve it when it = 0 to find max and min distance.

    I'm not sure if what I'm doing is right? Any help would be appreciated!
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  2. #2
    MHF Contributor Calculus26's Avatar
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    This is an ideal problem for the use of Lagrange multipliers.

    Are you in Calc3 ? If so use Langrange Multipliers if not get back to me
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