$\begin{array}{1 1}(A)\;(-5,2) \\(B)\;(2,-5) \\(C)\;(5,-2) \\(D)\;(-2,5) \end{array}$

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Since circle touches x-axis at $(3,0)$

The equation of circle be

$(x-3)^2+(y-0)^2+\lambda y=0$

As it passes through $(1,-2)$

Put $x=1 ; y=-2$

=> $(1-3)^2+(-2)^2+\lambda(-2)=0$

$\lambda=4$

equation of circle is

$(x-3)^2+y^{-8}=0$

Now, from the option $(5,-2)$ satisfies equation of circle.

Hence C is the correct answer.

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