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Question

Find the locus of the mid point of focal chords of the ellipsex2a2+y2b2=1

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Solution

Let P=(h, k) be the mid-point
equation of chord whose mid-point is given xha2+ykb21=h2a2+k2b21Since it is a focal chord,
it passes through focus, either (ae, 0) or (-ae, 0) If it passes through (ae, 0)
locus is exa=x2a2+y2b2 If it passes through (-ae, 0)
locus is exa=x2a2+y2b2

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