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Math Help - parametrically defined curve

  1. #1
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    parametrically defined curve

    I have a parametrically defined curve

    x(t) = \frac {1}{t}
    and
    y(t) = -2 + lnt

    I need to find the equation for the tangent line to the curve at the point defined by t = 1

    Now, i think i need to find \frac{dy}{dx}

    the dirivitive of x =  -\frac{1}{t^2} ?

    Would the dirivitive of y =  \frac{1}{t} ?

    then, i evaluate t= 1?

    then, take the dirivitive of dy again?

    then use point slope form?
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  2. #2
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    Re: parametrically defined curve

    Quote Originally Posted by icelated View Post
    I have a parametrically defined curve

    x(t) = \frac {1}{t}
    and
    y(t) = -2 + lnt

    I need to find the equation for the tangent line to the curve at the point defined by t = 1

    Now, i think i need to find \frac{dy}{dx}

    the dirivitive of x =  -\frac{1}{t^2} ?

    Would the dirivitive of y =  \frac{1}{t} ?

    then, i evaluate t= 1?

    then, take the dirivitive of dy again?

    then use point slope form?
    All your calculations are OK.

    \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}

    Plug in the terms you already have determined.

    Then use the point-slope-form of the equation of a straight line at t = 1
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  3. #3
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    Re: parametrically defined curve

    \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}

    Equation of the tangent line is :

    y(t)=\frac{dy}{dx}(t)\cdot x(t)+n
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