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Question

Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, x24+y22=1 from any of its foci?

A
(1,3)
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B
(2,3)
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C
(1,2)
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D
(1,2)
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Solution

The correct option is A (1,3)
We know that the locus of foot of the perpendiculars drawn from foci to any tangent of the ellipse is the auxiliary circle.
Auxiliary circle of an ellipse is x2+y2=a2
where a= Length of semi-major axis of the ellipse.

Thus the equation of the auxiliary circle of the ellipse x24+y22=1 is x2+y2=22=4
From the given options, (1,3) lies on the auxiliary circle.

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