Let P=(h, k) be the mid-point
∴ equation of chord whose mid-point is given xha2+ykb2−1=h2a2+k2b2−1Since 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