If  $\mathrm{p},{\mathrm{x}}_1,{\mathrm{x}}_2,{\mathrm{x}}_{3,}...$ and $\mathrm{q},{\mathrm{y}}_1,{\mathrm{y}}_2,{\mathrm{y}}_3,...$  form two infinite AP’s with common differences a and b respectively. The locus of $\text{p}\left(\alpha ,\beta \right),$  wher $\mathrm{\alpha }=\frac{{\mathrm{x}}_1+{\mathrm{x}}_2+...+{\mathrm{x}}_{\mathrm{n}}}{\mathrm{n}}$ and $\mathrm{p}=\frac{{\mathrm{y}}_1+{\mathrm{y}}_2+...+{\mathrm{y}}_{\mathrm{n}}}{\mathrm{n}}$ is