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求曲线的交点坐标是解析几何中一类广泛而繁琐的问题。但曲线的交点坐标在题目中常常只作为其他量的铺垫——过渡点,此时往往可通过“设而不解”的手法,绕过“求交点”这一迂道,直奔问题的终点。例1 推导点到直线的距离公式。求点P(x_0,y_0)到直线l:AX+By+C=O(A~2+B~2≠0)的距离d。(课本P49) 本题最自然的思路是:先求出点P在直线l上的射影点Q的坐标,再用距离公式d=|pQ|但求点Q的坐
Finding the coordinates of the intersection of curves is a broad and tedious problem in analytical geometry. However, the coordinates of the intersection point of the curve often only serve as a paving point for other quantities in the subject-transition point. At this time, it is often possible to bypass the intersection of the “intersection” and pass straight to the end of the problem. . Example 1 Derive the distance formula from point to line. Find the distance d from P(x_0,y_0) to the line l:AX+By+C=O(A~2+B~2≠0). (Textbook P49) The most natural idea of this question is: First, find the coordinates of the projective point Q of the point P on the straight line l, and then use the distance formula d=|pQ|