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Q.

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

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a

x216+y29=25

b

none of these

c

4x2+4y2−32x−24y+75=0

d

x216+y236=25

answer is B.

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Detailed Solution

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The center of the family of ellipse is (4, 3) and the distance of focus from the center is ae = 5/2. 

Hence, the locus is (x−4)2+(y−3)2=254

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