SAT1000 - P760

Geometry Level pending

As shown above, F1,F2F_1, F_2 are left and right focus of the hyperbola: x2a2y2b2=1 (a,b>0)\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\ (a,b>0) respectively, and B(0,b)B(0,b).

Line F1BF_1B intersects with the two asymptotes of the hyperbola at P,QP,Q, and the perpendicular bisector of PQPQ intersects with x-axis at point MM.

If MF2=F1F2|MF_2|=|F_1F_2|, then find the eccentricity of the hyperbola.

Let EE denote the eccentricity, submit 1000E\lfloor 1000E \rfloor.

Have a look at my problem set: SAT 1000 problems


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