Results 1 to 2 of 2

Math Help - Circle - line intersection point

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    2

    Circle - line intersection point

    Hello,
    I have a circle with radius "r" , centre (x1, y1). I have a straight line with starting point (x2, y2) end point (x3, y3). I want to know whether this line intersects with the circle? If yes what is/are the intersection points?

    Can I find out the same even for rectangle? and some irregular shape??

    With regards,
    Last edited by watashi; May 12th 2010 at 05:24 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by watashi View Post
    Hello,
    I have a circle with radius "r" , centre (x1, y1). I have a straight line with starting point (x2, y2) end point (x3, y3). I want to know whether this line intersects with the point? If yes what is/are the intersection points?

    Can I find out the same even for rectangle? and some irregular shape??

    With regards,
    Hi, watashi,

    I assume the word "point" in red above is supposed to be "circle."

    We can write the equation for the circle and equation for the line, and now we are solving a system of two equations in two variables, where one equation is quadratic and the other linear.

    For example, a unit circle centered at the origin, whose equation is x^2+y^2=1, and the points (-1,-2) and (1,2) defining the line y=2x.

    x^2+y^2=1

    y=2x

    Substitute the value of y into the first equation to get

    x^2+(2x)^2=1

    Now we have a quadratic equation in one variable, and we can solve for x.

    The reasoning for rectangles or other shapes is similar, except that we might not have a tidy equation to work with. Depending on the circumstances, we might elect to use approximation techniques instead.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Line / Circle intersection
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 28th 2011, 02:39 PM
  2. Intersection between circle and line
    Posted in the Geometry Forum
    Replies: 1
    Last Post: August 30th 2009, 01:19 PM
  3. Intersection Of A Line And Circle...
    Posted in the Pre-Calculus Forum
    Replies: 11
    Last Post: May 6th 2008, 03:11 AM
  4. Point line intersection
    Posted in the Geometry Forum
    Replies: 3
    Last Post: July 16th 2007, 05:40 AM
  5. Intersection of Circle and Line
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: May 11th 2007, 04:12 AM

Search Tags


/mathhelpforum @mathhelpforum