Concept:The general equation for a circle is (x - h)2 + (y - k)2 = r2, where ( h, k ) is the center and r is the radius.Calculation:The circle which touches both the axes in the first quadrant and the line y - 2 = 0 is shown in the figure.From the above figure, we can say that the diameter of the circle is 2.? r = 1 and the center of the circle is (1, 1).We know that the equation of the circle is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius.? (x - 1)2 + (y - 1)2 = 12? x2 - 2x + 1 + y2 - 2y + 1 = 12? x2 + y2 - 2x - 2y + 2 = 1? x2 + y2 - 2x - 2y + 1 = 0? The equation of the circle is x2 + y2 - 2x - 2y + 1 = 0.