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Find the locus of the mid points of the...

Find the locus of the mid points of the chords of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` which subtent a right angle at the origin.

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The correct Answer is:
`(x^2/a^(2)-y^(2)/b^(2)) (1/a^(2)-1/b^(2)) =x^(2)/a^(4)+y^(2)/b^(4)`
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