$\begin{array}{1 1}(A)\;(\frac{-3}{2},0) \\(B)\;(\frac{-5}{2},2) \\(C)\;(\frac{-3}{2},\frac{5}{2}) \\(D)\; (-4,0) \end{array}$

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Let the centre of the circle be $(h,2)$ then radius $=|h|$

equation of circle becomes $(x-h)^2+(y-2)^2=h^2$

As it passes through $(-1,0)$

=> $(-1-h)^2+4=h^2$

=> $h= \large\frac{-5}{2}$

Centre $\bigg( \large\frac{-5}{2},$$2\bigg)$

and $r= \large\frac{5}{2}$

Distance of centre from $(-4,0) $ is $\large\frac{5}{2}$

$\therefore $ It lies on the circle.

Hence D is the correct answer.

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