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对于解析几何中两曲线相交的问题,适当处理交点坐标是决定解题过程的繁简乃至解题成败的关键。处置两曲线的交点坐标的手段,其一是“解”.其二是“设”。于是,围绕着“解”与。“设”的不同选择,产生出不同的解题策略. 一、解而不设例1 过抛物线焦点的一条直线与它交于两点P、Q,通过点P和抛物线顶点的直线交准线于点M.求证:直线MQ平行于抛物线的对称轴。证明:设抛物线的方程为
For the problem of intersecting two curves in analytic geometry, the proper processing of the coordinates of the intersection is the key to determine the complexity of the problem-solving process and even the success or failure of the problem. One of the means to dispose of the coordinates of the intersections of the two curves is the “solution”. The second is the “setting.” So, around the “solution” and. The different choices of “set” produce different strategies for problem solving. First, solve without settling a line that crosses the focus of the parabola and intersect it at two points P, Q, and the straight line crosses the point P and the vertices of the parabola. Prove at point M. The straight line MQ is parallel to the symmetry axis of the parabola. Proof: Let parabolic equation be