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Find the locus of the foot of perpendic...

Find the locus of the foot of perpendicular from the centre upon any normal to line hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`.

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