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有关直线与圆锥曲线相交的问题,通常可联立直线与圆锥曲线的方程转化求解;当问题涉及到定比分点,且定比关系中涉及并且只涉及圆锥曲线上的一个点时,可用代点法~([1])简化运算,即首先由定比关系写出交点坐标,再代入圆锥曲线方程求解;当问题涉及到曲线的弦的中点时,则可应用点差法求解,即将直线被圆锥曲线所截得的弦的两端点坐标分别代入圆锥曲线方程,得到两个等式,再将这两等式作差,转化得到弦的中点坐标与直线斜率的关系,进而解决问题.
The problem of intersecting straight lines with conic curves can usually be solved by solving the equations of simultaneous straight lines and conic curves. When the problem involves determining the definite points, and the ratio relation involves only one point on the conic curve, Method ~ ([1]) to simplify the operation, that is, the relationship between the coordinates of the intersection of the first write out the intersection point, and then into the conic equation solution; when the problem involves the middle of the curve chord, you can apply the point difference method to solve, The two ends coordinates of the conic curve are respectively substituted into the conic curve equations, and two equations are obtained. Then the two equations are badly transformed to obtain the relationship between the midpoint coordinates of the chord and the slope of the straight line so as to solve the problem.