SAT1000 - P842

Geometry Level pending

As shown above, the ellipse has equation: x24+y22=1\dfrac{x^2}{4}+\dfrac{y^2}{2}=1, and line ll passing through P(0,1)P(0,1) intersects with the ellipse at point A,BA,B.

Then there exists a fixed point QQ so that the following equation always holds as ll rotates:


Then find the coordinate of QQ.

The coordinate of QQ is (x0,y0)(x_0,y_0). Submit 1000(2y0x0)\lfloor 1000(2y_0-x_0) \rfloor.

Have a look at my problem set: SAT 1000 problems


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