9

Part of 2006 China Second Round Olympiad

Problems(1)

2006 China Second Round Olympiad Test 1 #9

Source:

F_1, F_2

are the left and right foci of the ellipse

\frac{x^2}{16}+\frac{y^2}{4}=1

respectively, and point

P

\frac{|PF_1|}{|PF_2|}

x-\sqrt{3} y+8+2\sqrt{3}=0

. Find the value of ratio

\frac{|PF_1|}{|PF_2|}

\angle F_1PF_2

reaches its maximum value.

conicsellipseratiogeometry