1ãe=c/a=1/2,c=a/2,b^2=a^2-c^2=3a^2/4,
b=â3a/2,
设æ¤åæ¹ç¨ä¸ºï¼x^2/a^2-y^2/(3a^2/4)=1,
åçæ¹ç¨ä¸ºï¼x^2+y^2=3a^2/4,
ç´çº¿y=x+â6,代å
¥åæ¹ç¨ï¼
x^2+(x+â6)^2-3a^2/4=0,
2x^2+2â6x+6-3a^2/4=0,
å½ç´çº¿ååç¸åæ¶ï¼å¤å«å¼b^2-4ac=0,
a=2,
b=3*/4=3,c=1,
æ
æ¹ç¨ä¸ºï¼x^2/4+y^2/3=1.
2.设A(m,n), B(m,-n), BP: x=ky+4,代å
¥æ¤åæ¹ç¨ï¼
å¾(3k^2+4)y^2+24ky+36=0
y1=-n, y2=y1y2/y1=36/[-n(3k^2+4)],
ç»åk=(4-m)/n,
å¾y2=36/[-n( (3(m-4)^2+4n^2)/n^2]
åm^2/4 + n^2/3=1ï¼
å¾3m^2+4n^2=12ï¼
æ
y2=3n/(2m-5)
E(x2,y2), x2=ky2+4=(4-m)/n*3n/(2m-5)+4=(5m-8)/(2m-5)
AE: (y-n)/(x-m)=(y2-n)/(x2-m)=n(m-4)/[(m-1)(m-4)]=n/(m-1)
令Yï¼0, å¾x=1,
å³æè¿Q(1,0)
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