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Q.

The locus of mid points of the chords of the ellipse x2a2+y2b2=1 which pass through  the foot of a directrix 

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a

x2a2+y2b2=axe

b

x2a2+y2b2=exa

c

x2a2+y2b2=e

d

x2a2+y2b2=xae

answer is A.

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Detailed Solution

Given ellipsex2a2+y2b2=1

Let mid point of chord be  (x1,y1) 

Now equation  of chord is  S1=S11

xx1a2+yy1b2=x12a2+y12b2 since it passes through the point (ae,0) then (ae)x1a2+0=x12a2+y12b2  Locus of (x1 y1) is xae=x2a2+y2b2

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