SAT1000 - P819

Geometry Level pending

As shown above, given that F(1,0)F(1,0) is the right focus of the ellipse: x2a2+y2b2=1 (a>b>0)\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\ (a>b>0), OO is the origin.

If for all lines passing through FF which intersect with the ellipse at point A,BA,B, the following inequality always holds:

OA2+OB2<AB2|OA|^2+|OB|^2<|AB|^2

Then find the range of aa.

If the range can be expressed as: (l,+)(l,+\infty), submit 1000l\lfloor 1000l \rfloor.


Have a look at my problem set: SAT 1000 problems

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