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The auxiliary circle of a family of elli...

The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 and 6 units on the x- and the y-axis, respectively. If the eccentricity of all such ellipses is 1/2, then the locus of the focus will be

A

`x^2/16+y^2/9 = 25`

B

`4x^2 +4y^2 -32 x - 24 y +75= 0`

C

`(x^2)/(16)+y^2/9=25`

D

none of these

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The correct Answer is:
B
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