Results 1 to 6 of 6

Math Help - what is the line obtained from the equation of 2 intersecting circles?

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    64

    what is the line obtained from the equation of 2 intersecting circles?

    Hi, I am struggling with this problem . I do not know the properties of circles so well, so I gave the variables some values and drew, but I still don't get anything :-/. It would also be great if you could tell me how you know (what rule, etc.) you have used to answer the question. Thanks!

    The problem says:

    Let ax^2+ay^2+kx+ly+m=0, bx^2+by^2+px+qy+r=0 be two intersecting circles. Deviding the first equation by a and the second by b and subtracting, we obtain the equation of a line:

    (k/a-p/b)x+(l/a-q/b)y+(m/a-r/b)=0.

    What is this line?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Is it the line connecting the 2 points of intersection between the circles?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Is that a line?
    Does it exist for x^2 + y^2 = 1 vs. (x-5)^2 + y^2 = 1
    Under what conditions on k, a, p, b, and q does it not exist?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2010
    Posts
    64
    I am so lost... I drew and did not get a line connecting the two points of intersection, just a random line. Maybe I did it wrong, but I did it twice and got the same thing . Maybe there is a mistake there because it does not make much sense :-/
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    For starters, the intersection is 0 points, 1 point, 2 points, or infinitely many points in a circular locus. If you are doing something that leads to a linear equation, that seems kind of magic, doesn't it? Why would you believe that would work? It might. Feel free to prove it. Note: It does give the equation of the line, but it does NOT give the points of intersection.

    Second, not everything that looks like that is a circle. There must be relationships between the parameters. If you enforce the relationships, you will see that it is all quite a bit simpler. Expand (x-a)^{2} + (y-b)^{2} = r^{2}, and put it in that standard form. You will see the necessary relationships.

    Have you a particular numerical example that you find vexing?

    Exploration: If there is no intersection, what does it produce? It's a line perpendicular to what?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member abhishekkgp's Avatar
    Joined
    Jan 2011
    From
    India
    Posts
    495
    Thanks
    1
    Quote Originally Posted by juanma101285 View Post
    Hi, I am struggling with this problem . I do not know the properties of circles so well, so I gave the variables some values and drew, but I still don't get anything :-/. It would also be great if you could tell me how you know (what rule, etc.) you have used to answer the question. Thanks!

    The problem says:

    Let ax^2+ay^2+kx+ly+m=0, bx^2+by^2+px+qy+r=0 be two intersecting circles. Deviding the first equation by a and the second by b and subtracting, we obtain the equation of a line:

    (k/a-p/b)x+(l/a-q/b)y+(m/a-r/b)=0.

    What is this line?
    check out this link Radical axis - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Non intersecting circles...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 29th 2011, 12:23 PM
  2. Intersecting Circles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 7th 2011, 04:07 PM
  3. Intersecting Circles
    Posted in the Geometry Forum
    Replies: 2
    Last Post: March 26th 2011, 11:16 PM
  4. Two circles intersecting each other...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 25th 2010, 10:32 AM
  5. intersecting circles
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: March 14th 2009, 12:22 AM

Search Tags


/mathhelpforum @mathhelpforum