what is the equation of the circle whose centre lies on the line x-2y+2=0 and which touches the positive axes.

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  1. If it is tangent to the +x and +y axes, the center must also lie along the line
    x = y, so that it is equidistant from both axes. The two lines cross at
    y -2y +2 = 0, where y = 2.
    Therefore x = y = 2 at the center. The radius is R = 2, for tangency.
    The equation of the circle is
    (x-2)^2 + (y-2)^2 = R^2 = 4

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