The auxiliary circle ... - Ellipse

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

[A]x²/16 + y²/9=25

[B]4x² + 4y²-32x-24y+75 = 0

[C]x²/16 + y²/9=25

[D]none of these

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