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The normal at a point P on the hyperbola...

The normal at a point P on the hyperbola `b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2)` of eccentricity e, intersects the coordinates axes at Q and R respectively. Prove that the locus of the mid-point of QR is a hyperbola of eccentricity `(e )/(sqrt(e^(2)-1))`.

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