If a point P has coordinates (0, -2) and Q is any point on the circle ${\mathrm{x}}^2+{\mathrm{y}}^2-5\mathrm{x}-\mathrm{y}+5=0$, then the maximum value of (PQ)² is

$\begin{array}{l}\mathrm{P}(0,-2);\text{ circle is }{\mathrm{x}}^2+{\mathrm{y}}^2-5\mathrm{x}-\mathrm{y}+5=0\Rightarrow {\left(\mathrm{x}-\frac{5}{2}\right)}^2+{\left(\mathrm{y}-\frac{1}{2}\right)}^2=\frac{3}{2}\\ \Rightarrow \mathrm{Q}=\left(\frac{5}{2}+\sqrt{\frac{3}{2}}\cos \mathrm{\theta },\frac{1}{2}+\sqrt{\frac{3}{2}}\sin \mathrm{\theta }\right)\therefore (\mathrm{PQ}{)}^2=\frac{25}{2}+\frac{3}{2}+5\sqrt{\frac{3}{2}}(\cos \mathrm{\theta }+\sin \mathrm{\theta })\\ \Rightarrow \text{ Maximum of }(\mathrm{PQ}{)}^2=14+5\cdot \sqrt{\frac{3}{2}}(\sqrt{2})=14+5\sqrt{3}\end{array}$