问题
解答题
过点(0 ,-2 )的直线与抛物线y2=8x 交于A ,B 两点,若线 段AB 中点的横坐标为2 ,求线段AB 的长度.
答案
解:直线AB 的方程为y+2=kx ,
代入抛物线方程得k2x2- (4k+8 )x+4=0 .
∴,
又由题意得,解得k=2,或k=-1(不合题意,舍去),
∴
过点(0 ,-2 )的直线与抛物线y2=8x 交于A ,B 两点,若线 段AB 中点的横坐标为2 ,求线段AB 的长度.
解:直线AB 的方程为y+2=kx ,
代入抛物线方程得k2x2- (4k+8 )x+4=0 .
∴,
又由题意得,解得k=2,或k=-1(不合题意,舍去),
∴
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