Thooch Program!

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

1. $c$ is any arbitrary constant.

2. $\left(\alpha,\beta\right) = \left(3,4\right)$