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The auxiliary circle of a family of elli...

The auxiliary circle of a family of ellipse passes through the origin and makes intercepts of 8 and 6 units on the x- and y-axis, respectively. If the eccentricity of all such ellipses is 1/2 , then the locus of the focus will be `(x^2)/(16)+(y^2)/9=25` `4x^2+4y^2-32 y+75=0` `(x^2)/(16)+(y^2)/9=25` (d) None of these

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