math

Find the equation of the circle with center on the line x-2y+2=0 and which touchesboth positivex and positive y axes.

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  1. If the circle is tangent to both axes, you know its center is on the line y=x.

    So, now you know that the center is at the intersection of the two lines: (2,2)

    So, the circle has radius 2, and is

    (x-2)^2 + (y-2)^2 = 4

    See the graphs at

    http://www.wolframalpha.com/input/?i=plot+%28x-2%29^2+%2B+%28y-2%29^2+%3D+4%2C+x-2y%2B2+%3D+0%2C+y%3D0%2C+x%3D0

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