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Find the locus of the mid-point of the c...

Find the locus of the mid-point of the chord of the ellipse `(x^(2))/(16) + (y ^(2))/(9) =1,` which is a normal to the ellipse `(x ^(2))/(9) + (y ^(2))/(4) =1.`

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The correct Answer is:
`(9x^(2)+16y^(2)){(1)/((15x)^(2))+(1)/((40y)^(2))}=1`
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