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:

QAQB=PAPB\dfrac{|QA|}{|QB|}=\dfrac{|PA|}{|PB|}

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

×

Problem Loading...

Note Loading...

Set Loading...