A normal to the hyperbola (x^(2))/(a^(2)...

A normal to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` meets the axes in M and N and lines MP and NP are drawn perpendicular to the axes meeting at P. Prove that the locus of P is the hyperbola `a^(2)x^(2)-b^(2)y^(2)=(a^(2)+b^(2))^(2)`

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