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Find circle passing through two points and center lying on a line

  1. Jun 12, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the equation of a circle that passes through the points A(2,2) and B(5,3) and has its centre on the line y = x +1

    2. Relevant equations

    (x-h)^2 + (y-k)^2 = r^2

    3. The attempt at a solution

    can get 2 equations knowing the 2 points the circle passes through but still have 3 variables and am not sure how to use the equation for the centre

    (2-h)^2 + (2-k)^2 = r^2

    (5-h)^2 + (3-k)^2 = r^2


    How do I solve from here?
     
  2. jcsd
  3. Jun 12, 2008 #2
    What is h in terms of k?
     
  4. Jun 13, 2008 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Any perpendicular bisector of a chord is a radius- i.e. passes through the center of the circle.

    What is the center point of the interval AB? What is the slope of the line AB? What is the slope of a line perpendicular to that? What is the equation of the perpendicular bisector of AB? Where does that line intersect y= x+1?
     
  5. Jun 13, 2008 #4
    thanks!
     
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