If centre (1, 2), axes are parallel to co-ordinate axes, distance between the foci 8,  $\mathrm{e}=\frac{1}{\sqrt{2}}$ then equation of the ellipse is 

 

centre$=(\mathrm{h}, \mathrm{k})=(1, 2)$

distance b/w foci 2ae=8

$$\begin{gathered} \Rightarrow \mathrm{ae}=4 \\ given \mathrm{e}=\frac{1}{\sqrt{2}} \\ \Rightarrow \mathrm{a}=4\sqrt{2} \\ Now {\mathrm{b}}^2={\mathrm{a}}^2(1-{\mathrm{e}}^2)=32(1-\frac{1}{2})=32-16=16 \\ \therefore \mathrm{eq}ution of ellipse is \frac{{(\mathrm{x}-\mathrm{h})}^2}{{\mathrm{a}}^2}+\frac{{(\mathrm{y}-\mathrm{k})}^2}{{\mathrm{b}}^2}=1 \\ \frac{{(\mathrm{x}-1)}^2}{32}+\frac{{(\mathrm{y}-2)}^2}{16}=1 \end{gathered}$$