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Math Help - Parametric equation

  1. #1
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    Parametric equation

    Teh graph of xy-4x-2y-4=0 can be expressed as a set of parametric equations. If y = 4t/(t-3) and x= f(t), then f(t)=? The answer is t-1. Thanks for advice for tackling these in general.
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  2. #2
    Super Member Quacky's Avatar
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    Re: Parametric equation

    Why not just go ahead and make the substitution?

    xy-4x-2y-4=0

    [f(t)]\frac{4t}{t-3}-4[f(t)]-2\cdot\frac{4t}{t-3}-4=0

    Solve for [f(t)]
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  3. #3
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    Re: Parametric equation

    My simplication is getting really sloppy. I need some help with solving for x (f(t))
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  4. #4
    Super Member Quacky's Avatar
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    Re: Parametric equation

    First, separate the function, with terms including f(t) on the left side of the equation and terms without an f(t) component on the right. Then, take out a common factor of f(t) from the left. Write everything remaining on the left as one fraction, and everything on the right as one fraction. Then divide/multiply through as necessary so that you're left with something of the form f(t)=\cdots to simplify. If you need further help, please try this method yourself and show me how far you can get.
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  5. #5
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    Re: Parametric equation

    Quote Originally Posted by Quacky View Post
    Why not just go ahead and make the substitution?

    xy-4x-2y-4=0

    [f(t)]\frac{4t}{t-3}-4[f(t)]-2\cdot\frac{4t}{t-3}-4=0

    Solve for [f(t)]
    f(t)4t/t-3 - 4f(t) = 4(t-3)/-8t
    f(t) (4t/t-3 - 4)

    I then added the numbers between the parenthesis by multipling -4 by t-3. Then I multipled/divided accordingly to get it to the other side. I came up with t^(2)-6t+9/(-32t^(2) + 48)
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  6. #6
    Super Member Quacky's Avatar
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    Re: Parametric equation

    Quote Originally Posted by Quacky View Post
    Why not just go ahead and make the substitution?

    xy-4x-2y-4=0

    [f(t)]\frac{4t}{t-3}-4[f(t)]-2\cdot\frac{4t}{t-3}-4=0

    Solve for [f(t)]
    Quote Originally Posted by benny92000 View Post
    f(t)4t/t-3 - 4f(t) = 4(t-3)/-8t
    f(t) (4t/t-3 - 4)

    I then added the numbers between the parenthesis by multipling -4 by t-3. Then I multipled/divided accordingly to get it to the other side. I came up with t^(2)-6t+9/(-32t^(2) + 48)
    I still feel like you're not putting a full commitment into it.

    We had:

    [f(t)]\frac{4t}{t-3}-4[f(t)]-2\cdot\frac{4t}{t-3}-4=0

    I then advised that you split the terms so that terms involving an f(t) were on the left and terms without were on the right, and take a common factor of f(t)

    [f(t)](\frac{4t}{t-3}-4)=4+\frac{8t}{t-3}

    My next piece of advice was to rewrite everything on each side over a common denominator.

    [f(t)]\cdot\frac{4t-4(t-3)}{t-3}=\frac{4(t-3)+8t}{t-3}

    Now we can just multiply through by (t-3), as my previous response implied, to get:

    [f(t)]\cdot [4t-4(t-3)]=[4(t-3)+8t]

    I've done the majority for you now - see if you can finish.
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  7. #7
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    Re: Parametric equation

    I fnally came to the right answer. Thanks
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