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anonymous

  • 5 years ago

1. Eliminate the parameter to find the Cartesian equation for the curve: y = e^(2t) + 1 and x = e ^t .

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  1. amistre64
    • 5 years ago
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    so how do we combine parameter equations into a single equation?

  2. anonymous
    • 5 years ago
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    would it be y = x^(2) + 1 bc (e^t)^2 = e^2t

  3. anonymous
    • 5 years ago
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    and x = e^t

  4. anonymous
    • 5 years ago
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    ???

  5. amistre64
    • 5 years ago
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    dunno, depends on if y is a function of x :)

  6. amistre64
    • 5 years ago
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    y is a function of "t"; so I would assume its independant of "x"

  7. amistre64
    • 5 years ago
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    Wikipedia: "Converting a set of parametric equations to a single equation involves eliminating the variable t from the simultaneous equations . If one of these equations can be solved for t, the expression obtained can be substituted into the other equation to obtain an equation involving x and y only. If x(t) and y(t) are rational functions then the techniques of the theory of equations such as resultants can be used to eliminate t. In some cases there is no single equation in closed form that is equivalent to the parametric equations."

  8. amistre64
    • 5 years ago
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    solve for "t" and substitute it into the other equation.... is what I think it says :)

  9. amistre64
    • 5 years ago
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    x = e^t ln(x) = t y = e^(2ln(x)) +1 is what I make of it

  10. anonymous
    • 5 years ago
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    ok thanks

  11. amistre64
    • 5 years ago
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    that can be simplified probably :) y = e^(2ln(x)) +1 y = e^(ln(x^2)) +1 y = x^2+1 does that make sense?

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