高二解析几何已知椭圆x^2／9+y^2／5=1（1）动直线L垂直于x轴,交椭圆与E、F两点,E、F两点分别和椭圆长轴的两

(1)
a = 3,A(-3,0),B(3,0)
动直线L:x = e
E(e,f),F(e,-f)
e²/9 + f²/5 = 1 (i)
AE的方程:(y - 0)(f - 0) = (x + 3)/(e + 3) (ii)
BF的方程:(y - 0)(-f -0) = (x - 3)/(e - 3) (iii)
由(ii)(iii)得:x = 9/e,y = 3f/e = 3f/(9/x) = fx/3
e = 9/x
f = 3y/x
代入(i)并整理:
x²/9 - y²/5 = 1
(2)
椭圆长轴的两个端点分别为A,B; 作椭圆长轴的垂线与椭圆交于E,F两点,直线AE,BF交点的轨迹称为椭圆的“伴随曲线”,x²/a² + y²/b² = 1的“伴随曲线”为x²/a² - y²/b² = 1

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