Let the point be $\left(\mathrm{h},\mathrm{k}\right)$

Distance between the two points will be $=\sqrt{{\left(\mathrm{h}-3\right)}^2+{\left(\mathrm{k}+2\right)}^2}$

$\Rightarrow 4=\sqrt{{\left(\mathrm{h}-3\right)}^2+{\left(\mathrm{k}+2\right)}^2}$

Squaring both sides we get,

$16={\mathrm{h}}^2+9-6\mathrm{h}+{\mathrm{k}}^2+4\mathrm{k}+4$

$\Rightarrow {\mathrm{h}}^2-6\mathrm{h}+{\mathrm{k}}^2+4\mathrm{k}-3=0$

Therefore, required locus is ${\mathrm{x}}^2+{\mathrm{y}}^2-6\mathrm{x}+4\mathrm{y}-3=0$