SAT1000 - P766

Geometry Level pending

As shown above, the left and 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) are F1(c,0),F2(c,0)F_1(-c,0), F_2(c,0).

If there exists point PP such that asinPF1F2=csinPF2F1\dfrac{a}{\sin \angle PF_1F_2}=\dfrac{c}{\sin \angle PF_2F_1}, find the range of the eccentricity of the ellipse.

The range can be expressed as (l,r)(l,r). Submit 1000(2rl)\lfloor 1000(2r-l) \rfloor.

Have a look at my problem set: SAT 1000 problems


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