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Circumferences and lines

  1. May 5, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the angular coefficient of the line that is tangent to the following circumferences:
    [tex](x - 17)^{2} + y^{2} = 16[/tex]
    [tex]x^{2} + y^{2} = 16[/tex]

    2. Relevant equations


    3. The attempt at a solution

    I tried everything but nothing is working, please help me.
     
  2. jcsd
  3. May 5, 2010 #2

    Mark44

    Staff: Mentor

    What did you try? Have you drawn a picture of the two circles (not circumferences)?

    By "angular coefficient" do you mean slope?
     
  4. May 5, 2010 #3
    Yeh I mean slope.

    here is a picture:

    [PLAIN]http://img94.imageshack.us/img94/2910/58393508.png [Broken]

    I tried to make a system of equations such that: the distance between the center of the circumferences and the line is equal to 4 (that is the radius of the circumferences). But I end up to something like |17a + c| = |c| (considering the line as ax + by + c = 0), but it doesn't help me.

    I tried to make two systems:
    1: using the equation of the first circumference and the equation of the line
    2: using the equation of the second circumference and the equation of the line
    then I shared some variables between these systems (a and b, considering y = ax + b as the line). But the equations become very complicated and I think it's not the easiest way.

    Someone can help me?
     
    Last edited by a moderator: May 4, 2017
  5. May 5, 2010 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Writing equations probably isn't the easiest way to solve it. Why don't you draw some right triangles in your picture?
     
  6. May 5, 2010 #5
    Thank you, you helped me alot, now I solved.
     
  7. May 6, 2010 #6

    Mark44

    Staff: Mentor

    I hope you realize that there is not just one tangent line that touches the circles. I count four of them.
     
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