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Math Help - Eliminate the parameter to find a Cartesian equation

  1. #1
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    Eliminate the parameter to find a Cartesian equation

    Hey, I'm new to the boards, and I figured I'd ask you knowledgeable people about my problem. Thankyou!

    Directions: Eliminate the parameter to find a cartesian equation in terms of x of the following curve.

    x(t)= 6ln(5t) , y(t)= √t

    Thanks!
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  2. #2
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    Hello Inexcess

    Welcome to Math Help Forum!
    Quote Originally Posted by Inexcess View Post
    Hey, I'm new to the boards, and I figured I'd ask you knowledgeable people about my problem. Thankyou!

    Directions: Eliminate the parameter to find a cartesian equation in terms of x of the following curve.

    x(t)= 6ln(5t) , y(t)= √t

    Thanks!
    You have:

    x = 6\ln (5t)

    \Rightarrow \ln(5t) = \frac{x}{6}

    \Rightarrow 5t = e^{\frac{x}{6}}

    \Rightarrow t = \tfrac15e^{\frac{x}{6}}

    \Rightarrow \sqrt{t} = \sqrt{\tfrac15e^{\frac{x}{6}}}

    which can be written as

     \sqrt{t}= \tfrac{1}{\sqrt5}e^{\frac{x}{12}}

    But y = \sqrt{t}

    So a Cartesian equation is

    y =\tfrac{1}{\sqrt5}e^{\frac{x}{12}}

    Grandad
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  3. #3
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    Thank you! I greatly appreciate it.
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