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Math Help - find equation of circle

  1. #1
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    find equation of circle

    If AB is the diameter of a circle and P another point on the circumference then Euclidean Geometry tells us that angle APB=90 degrees. Use this fact to show that the equation of the circle whose diameter has endpoints
    A(x1,x2) and B(x2,y2) is (x-x1)(x-x2)+(y-y1)(y-y2)=0

    (all the numbers above should be sub script, sorry)

    Any help greatly appreciated.
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  2. #2
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    Quote Originally Posted by slaypullingcat View Post
    If AB is the diameter of a circle and P another point on the circumference then Euclidean Geometry tells us that angle APB=90 degrees. Use this fact to show that the equation of the circle whose diameter has endpoints
    A(x1,x2) and B(x2,y2) is (x-x1)(x-x2)+(y-y1)(y-y2)=0

    (all the numbers above should be sub script, sorry)

    Any help greatly appreciated.
    If P is the point on the circle, then find the slope of the line AP and BP.
    Since angle APB 90 degrees the product of the slopes should be -1.
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