$$\begin{gathered} Given parabola {\mathrm{y}}^2=32\mathrm{x} \\ \Rightarrow 4\mathrm{a}=32 \\ \Rightarrow \mathrm{a}=8 \\ Let ({\mathrm{x}}_1,{\mathrm{y}}_1) ,\left({\mathrm{x}}_{2,}{\mathrm{y}}_2\right) be two points on given parabola \\ \mathrm{Focus} = (8,0) \end{gathered}$$

$$\begin{gathered} \overline{)\left|{\mathrm{x}}_1+\mathrm{a}\right|=10} and \left|{\mathrm{x}}_2+a\right|=10 \\ \left|{\mathrm{x}}_1+8\right|=10 \Rightarrow {\mathrm{x}}_2=\pm 2 \\ \Rightarrow x_1 =\pm 2 then {y_2}^2 =32\times 2 \\ then {{\mathrm{y}}_1}^2=32\times 2 \Rightarrow {y_2}^2 =64 \\ \Rightarrow {{\mathrm{y}}_1}^2=64 \end{gathered}$$

$Now 2({{\mathrm{x}}_1}^2+{{\mathrm{x}}_2}^2+{{\mathrm{y}}_1}^2+{{\mathrm{y}}_2}^2)=2(4+4+64+64)=272$