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A senior high school math problem about ellipse
The directrix x=-3 and the ellipse c=2.

M(-3,0),F 1(-2,0)

The straight line of MAB is y=k(x+3).

Simultaneous elliptic equation and MAB linear equation eliminate y to get the quadratic equation of x;

Vieta theorem is used to find the sum of two xa+xb and the product of two xa*xb (because it is simplified later), both of which are expressions of k;

It is necessary to prove that BF 1 c * * * line is equivalent to BF1slope =BC slope, which can simplify the proof.