# Thooch Program!

Geometry Level 5

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

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