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A variable tangent to the ellipse (x^(2)...

A variable tangent to the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` makes intercepts on both the axes. The locus of the middle point of the portion of the tangent between the coordinate axes is

A

`(x^(2))/(b^(2))+(y^(2))/(a^(2))=1`

B

`(a^(2))/(x^(2))+(b^(2))/(y^(2))=1`

C

`b^(2)x^(2)+a^(2)y^(2)=4`

D

`(a^(2))/(x^(2))+(b^(2))/(y^(2))=4`

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The correct Answer is:
D
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