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在解析几何中,直线与圆锥曲线的位置关系是经久不衰的热点,在设直线方程时,我们总习惯用与直线斜率有关的直线方程,即点斜式和斜截式,这当然没有错,但由于这些直线方程不能表示与X轴垂直的直线,故在解答时,往往会出现下列情况,容易忽视对斜率不存在的情形或者运算较繁,需要讨论几种情形。如果当我们知道直线的斜率不为0时可将其方程设为x=my+n。这样不仅可以避免讨论直线斜率的存在性,而且有时可大大简化运算。
In analytic geometry, the relationship between the straight line and the conic is an enduring hot spot. When setting up the straight line equation, we always use the straight line equation related to the slope of the straight line, that is, point oblique and oblique cut. This is certainly not wrong However, since these linear equations can not represent a straight line perpendicular to the X-axis, the following situations often occur when solving the problem, and it is easy to overlook the situation that the slope does not exist or the calculation is complicated. There are several situations to be discussed. If we know that the slope of a straight line is not 0, we can set its equation to x = my + n. This not only avoids the discussion of the existence of linear slopes, but sometimes greatly simplifies the calculation.