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Geometry Level pending

Suppose points F1 and F2 are the left and right foci of the ellipse x 2 / 16 + y 2 / 4 = 1 x^2/16 + y^2/4 = 1 respectively and the point P is on the line x 3 y + 8 + 2 3 = 0 x - √3y + 8 + 2*√3=0 . When Angle F1PF2 reaches the maximum then the value of ratio | P F 1 P F 2 \frac{PF1}{PF2} | is equal to

2 + 1 √2 +1 None of these 3 1 √3 -1 2 1 √2 -1

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