SAT1000 - P759

Geometry Level 2

As shown above, the line: x3y+m=0 (m0)x-3y+m=0\ (m \neq 0) intersects with the two asymptotes of the hyperbola:

x2a2y2b2=1 (a>0,b>0)\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\ (a>0,b>0) at point A,BA,B.

If point PP is at (m,0)(m,0) and PA=PB|PA|=|PB|, 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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