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As shown above, the line: x−3y+m=0 (m≠0)x-3y+m=0\ (m \neq 0)x−3y+m=0 (m=0) intersects with the two asymptotes of the hyperbola:
x2a2−y2b2=1 (a>0,b>0)\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\ (a>0,b>0)a2x2−b2y2=1 (a>0,b>0) at point A,BA,BA,B.
If point PPP is at (m,0)(m,0)(m,0) and ∣PA∣=∣PB∣|PA|=|PB|∣PA∣=∣PB∣, find the eccentricity of the hyperbola.
Let EEE denote the eccentricity, submit ⌊1000E⌋\lfloor 1000E \rfloor⌊1000E⌋.
Have a look at my problem set: SAT 1000 problems
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