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Math Help - Curve defined by two implicit functions

  1. #1
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    Curve defined by two implicit functions

    The curve r(t) passing through the point is defined implicitly by the equations:

    x^2y + y^2x + xyz + z^2 = 4
    x + y + z = 3

    i) Find the equation of the tangent line to this curve at the given point.
    ii) Assume that we may choose x = t as the parameter. Find formulae for dy/dt and d^2y/dt^2.

    I'm not sure how to tackle these questions. For i), can I use either of the two equations?
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  2. #2
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    if x=t then dy/dt=dy/dx

    Well, if x=t, then what you are really looking for are the first and second derivatives of y with respect to x. Start by simplifying x^2y + y^2x + xyz + z^2=xy(x+y+z) + z^2=3xy+z^2=4, and then substituting z=3-x-y to get x^2-6x+5xy-6y+y^2+5=0. Next differentiate implicitly to find \frac{dy}{dx}: 2x-6+5xy'+5y-6y'+2yy'=0. Isolate y' and repeat the process to get y''. This should be enough to get you started.
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  3. #3
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    Quote Originally Posted by My Little Pony View Post
    The curve r(t) passing through the point is defined implicitly by the equations:

    x^2y + y^2x + xyz + z^2 = 4
    x + y + z = 3

    i) Find the equation of the tangent line to this curve at the given point.
    ii) Assume that we may choose x = t as the parameter. Find formulae for dy/dt and d^2y/dt^2.

    I'm not sure how to tackle these questions. For i), can I use either of the two equations?
    Didn't you already post this

    http://www.mathhelpforum.com/math-he...ine-curve.html
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