If the normal at \((x_i,y_i),~i = 1,2,3,4\) on a hyperbola \(xy=c^2\) meet at the point \(\left(\alpha,\beta\right)\), then, find the value of \(:\!-\)

\(\displaystyle \sum x_i +\sum y_i +\sum x_i^2 +\sum y_i^2\)

**Details and Assumptions**

\(c\) is any arbitrary constant.

\(\left(\alpha,\beta\right) = \left(3,4\right)\)

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