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Math Help - Parametric Equations- Take 2

  1. #1
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    Parametric Equations- Take 2

    The graph of the parametric equations



    meets the graph of the parametric equations



    at two points. Find the slope of the line between these two points.






    So far, I tried equating x's and y's, but got

    cos(t) = 2+ 4cos(s)
    sin(t)= 3+ 4sin(s)

    How can I add those and continue from there? Thank you!
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  2. #2
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    Re: Parametric Equations- Take 2

    You are trying to find relationships between s and t. That is very difficult. Instead, try to find relationships between x and y. What do you get from x^2+y^2 (use the first parametric equation)? What about (x-2)^2+(y-3)^2 (use the second parametric equation)?
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  3. #3
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    Re: Parametric Equations- Take 2

    Thanks, Slip! Using the cos^2+sin^2=1 theorem I ended up with

    4 cos(s) = -7 -6 sin (s)

    So x= 2 + -7 - 6 sin(s)

    And adding that to the other equation, y=3+4sin(s), I ended up with

    6y + 4x = -2
    And from this I can get y= -2/3 x -1/3

    So is the slope -2/3? I took an intuitive approach and aren't 100% sure if I did it right
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  4. #4
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    Re: Parametric Equations- Take 2

    That is correct
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  5. #5
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    Re: Parametric Equations- Take 2

    Thanks again!
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