Find the equation of a circle that passes through the points (6,3) ans (-4,-3) and whose center lies on the line y=2x-7

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  1. Find the midpoint of the 2 given points
    that would be (1,0)
    - slope of the line joining those 2 points = 6/10 = 3/5
    - so the slope of the right-bisector of the segment joining the two points is -5/3
    - equation of that bisector is y = -(5/3)x + b
    (1,0) lies on it
    0 = -5/3 + b
    b = 5/3
    the centre must lie on y = -(5/3)x + 5/3 and y = 2x = 7

    solve the two equations to find the centre, take it from here

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