If the normals at \( (x, y), i=1,2,3,4 \) on the rectangular hyperb...

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If the normals at \( (x, y), i=1,2,3,4 \) on the rectangular hyperbola, \( x y=c^{2} \), meet at the point \( (\alpha, \beta) \) show
\( \mathrm{P} \) that \( \sum x_{i}^{2}=a^{2} \)

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