SOLUTION: how to solve this find the equation of the circle describe here.. {{the circle is tangent to the line 2x-y=3 at the point (2,1) and the center is on the x-axis}} tnx.

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at the point of tangency, the radius of the circle is perpendicular to the tangent line

perpendicular lines have slopes that are negative reciprocals

so the slope of a radius is -1/2 ___ it passes through (2,1) ___ and the other end is on the x-axis (y = 0)

the center of the circle is (4,0) ___ this is down 1 and over 2 from (2,1)

by Pythagoras, the radius squared is 2^2 + 1^2 ___ so r^2 = 5

the equation of the circle is ___ (x - 4)^2 + (y - 0)^2 = 5