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Intersection of line and circle

  1. Oct 20, 2005 #1
    I'm trying to find the points of intersection
    of line and circle with equations:

    (x-p)^2 + (y-q)^2 = r^2
    (y-y1)*(x2-x1)-(x-x1)*(y2-y1)=0

    but i can't handle with this. Can anyone help me?
     
  2. jcsd
  3. Oct 20, 2005 #2
    What do you know about the circle's dimensions?
     
  4. Oct 21, 2005 #3

    mathman

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    Science Advisor
    Gold Member

    Your second equation (the line) can be simplified to look like y=mx+b (I assume x1, x2,y1,y2 are constants). Substitute mx+b for y in the first equation. You now have a quadratic in x. Solve for x, 2 real roots gives points of intersection, 1 root is tangency point, 0 real roots means no intersection. If x roots are real, use second equation to get y values.

    Special case x1=x2, then x comes right out of second equation and 2 values of y can be found. Above comments about real roots and intersections apply. Line happens to be vertical.
     
  5. Aug 10, 2007 #4
    I see how the case where the line is not vertical works but I don't see what you would do in the case where it is vertical. Can you explain in a little more detail?
     
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