Since it is an arbitrary point, let s be the vertex of hyperbola, then s, m, n, m, n coincide, and OP=OQ. Because (1/om+1/on) (op+OQ) ≥ 4, 2OP×2/OM≥4 and OP≥OM. And because MP is parallel to. /a? )=√((a? +b? )/a? )≥√(2a? /a? ) =√2. So the range of hyperbola eccentricity is e∈[√2, +∞).