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# Find the equation of the circle which touches $x$-axis and whose centre is $(1, 2)$

• The equation of a circle with center $(h,k)$ and radius $r$ is $(x - h)^2 + (y - k)^2 = r^2$
Given that the circle touches the $x$-axis $\rightarrow$ radius of the circle $=k$.
Given that $(h,k) = (1,2) \rightarrow$ the equation of the circle is $(x-1)^2 + (y-2)^2 = 2^2 = 4$