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Math Help - Find the parametric equations of the tangent line to a line (Answer included)

  1. #1
    s3a
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    Find the parametric equations of the tangent line to a line (Answer included)

    The question and answer are attached. I'm having trouble with the material in this course (Intermediate Calculus). I'm also particularly having trouble with parametric equations which I believe I should know already but I don't so please illustrate how to do this problem.

    Any help would be GREATLY appreciated!
    Thanks in advance!
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  2. #2
    Super Member TheChaz's Avatar
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    Re: Find the parametric equations of the tangent line to a line (Answer included)

    Uh... take the derivative of each component, then plug in "t"... ?!?!

    I assume by "correct answers", you mean that there is a one-to-one correspondence between the blanks and the numbers {2, 28, 13, 0, -6, 9}...

    x = 9 + 0t. There you go.
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    s3a
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    Re: Find the parametric equations of the tangent line to a line (Answer included)

    What you said wasn't very thorough (just saying) but it gave me enough to figure it out by myself. But still, thank you very much!

    If anyone else cares:
    Take the slope/derivative of the x, y or z component of the curve and that's the slope for the same component of the tangent's set of parametric equations, for the intercept of the tangent lines' components, insert t = 0 prior to differentiating the curve's components and that constant is the y-intercept.
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    Super Member TheChaz's Avatar
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    Re: Find the parametric equations of the tangent line to a line (Answer included)

    Quote Originally Posted by s3a View Post
    1.What you said wasn't very thorough (just saying) but it gave me enough to figure it out by myself. But still, thank you very much!

    If anyone else cares:
    Take the slope/derivative of the x, y or z component of the curve and that's the slope for the same component of the tangent's set of parametric equations, for the intercept of the tangent lines' components, insert t = 0 prior to differentiating the curve's components and that constant is the y-intercept.
    1. By design. This problem should take no more than 2 minutes.
    x'(t) = 28cos(7t)
    y'(t) = -28sin(7t)
    z'(t) = 9.

    x(0) =
    y(0) =
    z(0) =

    etc.

    But glad you got it!
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