已知抛物线C：x2=4y的焦点为F,过点F作直线l交抛物线C于A、B两点；椭圆E的中心在原点,焦点在

已知抛物线C：x2=4y的焦点为F,过点F作直线l交抛物线C于A、B两点；椭圆E的中心在原点,焦点在

(1) x² = 4y = 2py,p = 2F(0,1)b = 1,e² = c²/a² = (a² - b²)/a² = 1 - b²/a² = 1 - 1/a² = 3/4a² = 4x²/4 + y² = 1(2)设A(a,a²/4),B(b,b²/4),AB的方程:(y - b²/4)/(a²/4 - b²/4) = (x - b)/a - b)4y = (a + b)x - ab过F(0,1):ab = -4 (i)y = x²/4y' = x/2L1:y - a²/4 = (a/2)(x - a) (ii)L2:y - b²/4 = (b/2)(x - b) (iii)联立(ii)(iii):x = (a + b)/2,y = ab/4 = -4/4 = -1M((a+b)/2,-1)AB的斜率p = (a²/4 - b²/4)/(a - b) = (a + b)/4FM的斜率q = (-1 - 1)/[(a + b)/2 - 0) = -4/(a + b)pq = -1,AB垂直MF

这个问题的回答的对

如以上回答内容为低俗、色情、不良、暴力、侵权、涉及违法等信息，可以点下面链接进行举报！

点此我要举报以上问答信息