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Math Help - Parametric equation.. life application tricky...

  1. #1
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    Parametric equation.. life application tricky...

    I am having some difficulty understanding this question i would appreciate all the help i can get solving it.

    a track on a hill side leading to a house, is in the shape of a smooth curve given parametrically by x=(3-2t)^2 y=(t^3-2t)

    a copy of the hillside is placed in the x-y plane so that a post (P) on the northern end of the track is located at the point where t=2. the hill also follows the equation x^2+4y^2-4x-12y-12=0 find


    1) the slope of the track at point (P) where the post is located.

    2) the equation that can be used to represent the straigh line from the point P to the origin on the x-y plane

    3)An expression for the steepness of the hill..

    i have though about this but not sure what angle to take this from.. i would really appreciate any help i can get.
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  2. #2
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    [QUOTE=sigma1;489557]I am having some difficulty understanding this question i would appreciate all the help i can get solving it.

    a track on a hill side leading to a house, is in the shape of a smooth curve given parametrically by x=(3-2t)^2 y=(t^3-2t)

    a copy of the hillside is placed in the x-y plane so that a post (P) on the northern end of the track is located at the point where t=2. the hill also follows the equation x^2+4y^2-4x-12y-12=0 find


    1) the slope of the track at point (P) where the post is located.[/tex]
    the slope is given by \frac{dy}{dx}= \frac{\frac{dy}{dt}}{\frac{dx}{dt}}.

    2) the equation that can be used to represent the straigh line from the point P to the origin on the x-y plane
    Since P is where t= 2, use the parametric equations to find (x, y) at P and then find the equation of the line from (0, 0) to (x, y)

    3)An expression for the steepness of the hill..

    i have though about this but not sure what angle to take this from.. i would really appreciate any help i can get.
    The equation, f(x,y)x^2+4y^2-4x-12y-12=0, of the hill is the equation of a circle in the xy-plane which I presume is the outline of the base of the hill. There is no information given about height or steepness. Unless we are to presume that this is a side projection and y is the height. In that case, the steepness of the hill at any point is the length of the gradient of f(x,y) at that point.
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  3. #3
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    thanks for the steps. but could you show me how to do the steps you have just outline. this topic is somewat new to me...
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