SAT1000 - P811

Geometry Level pending

As shown above, given that ellipse E:x2t+y23=1 (t>3)E: \dfrac{x^2}{t}+\dfrac{y^2}{3}=1\ (t>3), point AA is the left vertex of EE, and line ll whose slope is k (k>0)k\ (k>0) intersects with EE at point A,MA,M, point NN is a point on EE such that MANAMA \perp NA.

If 2AM=AN2|AM|=|AN|, find the range of kk as tt changes.

If 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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