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Help Circle Geometry

  1. Feb 7, 2009 #1
    1. The problem statement, all variables and given/known data

    In the diagram alongside, A(2,3) and B(-1,6) lie on the circle with centre M(c,d).
    M is also a point on the straight line defined by 2x + 5y + 1=0. The diagram is on the attached doc file.

    Calculate the co-ordinates of M.

    2. Relevant equations

    analytical methods only!

    3. The attempt at a solution
    Im realy stuck:frown:
     

    Attached Files:

  2. jcsd
  3. Feb 7, 2009 #2

    Tom Mattson

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    Staff Emeritus
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    Gold Member

    You have 3 unknowns (c, d, and the radius r of the circle), so you need 3 equations to find them. Try to answer the following questions. They should help you.

    1.) What is the standard form of the equation form of a circle with center (c,d) and radius r?
    2.) What do you get when you plug the point (x,y)=(-1,6) into that equation?
    3.) What do you get when you plug the point (x,y)=(2,3) into that same equation?
    4.) What do you get when you plug the point (x,y)=(c,d) into the equation of the given line?

    That should get you started.
     
  4. Feb 8, 2009 #3
    Thank you I got it. M is (-3,1):biggrin:
     
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