SAT1000 - P842

Geometry Level pending

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

Then there exists a fixed point $Q$ so that the following equation always holds as $l$ rotates:

$\dfrac{|QA|}{|QB|}=\dfrac{|PA|}{|PB|}$

Then find the coordinate of $Q$ .

The coordinate of $Q$ is $(x_0,y_0)$ . Submit $\lfloor 1000(2y_0-x_0) \rfloor$ .

Have a look at my problem set: SAT 1000 problems