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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


    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


    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


    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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