SAT1000 - P810

Geometry Level pending

As shown above, the ellipse $C: \dfrac{x^2}{4}+\dfrac{y^2}{3}=1$ , $O(0,0), P(2,1)$ , line $l$ intersects with $C$ at point $A,B$ , and line $OP$ bisects segment $AB$ .

If the area of $\triangle APB$ reaches the maximum value, then find the equation of line $l$ .

The equation of the line can be expressed as $y=kx+b$ , submit $\lfloor 1000(k+b) \rfloor$ .

Have a look at my problem set: SAT 1000 problems