圆锥曲线是圆、椭圆、双曲线和抛物线的统称,它是平面解析几何研究的主要对象.在直线与圆锥曲线的位置关系中,涉及弦的问题特别多,其中尤以过定点弦的问题更是五彩缤纷,本文就圆锥曲线对称轴上定点弦相关性质做一点探究.问题1如图1,设过抛物线y~2=2px(p>0)对称轴上的定点M(m,0)(m≠0)的直线l交抛物线于A、B两点.问:在x轴上是否存在定点N,使得 The conical curve is a general term for circles, ellipses, hyperbolas, and parabolas. It is the main object for the study of plane analytical geometry. In the positional relationship between straight lines and conic curves, the problems involving strings are particularly large, and especially the problems of over-pointing strings. This is colorful, this article does a little research on the properties of the fixed point chord on the axis of symmetry of the conic section. Problem 1 As shown in Fig. 1, we set the fixed point M(m,0) (m,0) on the axis of symmetry of y~2=2px(p>0). The line l of ≠ 0) intersects the two points A and B. Q: Is there a fixed point N on the x-axis, making