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[" The auxiliary circle of a family of ellipse passes through origin and makes intercepts of "8" and "6" units on "],[" the x-axis and y-axis respectively.If eccentricity of all such family of ellipse is "(1)/(2)," then locus of the "],[" focus will be "],[[" 1) "(x^(2))/(16)-(y^(2))/(9)=25," 2) "4x^(2)+4y^(2)-32x-24y+75=0," 3) "(x^(2))/(16)+(y^(2))/(16)=25," 4) none of these "]]

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