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If the locus of the middle point of the portion of a tangent of the ellipse `x^2/a^2+y^2/b^2=1` included between the axes is `(a^2/x^2)+ (b^2/y^2)=k` , then the value of k is

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
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