Match the following

$\text{ A) }{\mathrm{x}}^2-{\mathrm{y}}^2=2\mathrm{x}\Rightarrow (\mathrm{x}-1{)}^2-{\mathrm{y}}^2=1$ a rectangular hyperbola
$\text{ B) }\mathrm{PA}+\mathrm{PB}=\mathrm{k};\mathrm{k}>\mathrm{AB}\Rightarrow$locus of P is ellipse
$\text{ C) }|\mathrm{z}-\mathrm{i}/2|=\mathrm{m}|\mathrm{z}+1|;\mathrm{M}=1\to$a straight line
$\mathrm{M}\ne 1\to$a circle
$\text{ D) }{\mathrm{x}}^2+{\mathrm{y}}^2=625\text{; locus of }(-1+75\mathrm{x},-75\mathrm{y})\text{ is }$$\frac{(\mathrm{x}+1{)}^2}{{75}^2}+\frac{{\mathrm{y}}^2}{{75}^2}=625$