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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 x^2 = 4`

D

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

Text Solution

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The correct Answer is:
D
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