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Question

The locus of mid-point of focal chords of the ellipse x2a2+y2b2=1 is:

A
x2a2+y2b2=exa
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B
x2a2y2b2=exa
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C
x2+y2=a2+b2
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D
None of these
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Solution

The correct option is A x2a2+y2b2=exa
Let (h,k) be the mid point of a focal chord. Then its equation is T=S1

xha2+kyb21=h2a2+k2b21

Since it passes through (ae,0)

haea2=h2a2+k2b2

Locus of (h,k) is x2a2+y2b2=xea

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