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解析几何中某些较复杂的两曲线相交问题,若能利用方程组的等价转化,可以使问题简单化,易于得解.下面举数例来说明这一思想方法。例1 试判断直线l:Ax+By+C=0与椭圆C:x~2/a~2+y~2/b~2=1的位置关系. 解直线l与椭圆C相交、相切和相离,分
Some of the more complex two-curve intersections in analytic geometry can be simplistic and easy to solve if they can be converted using the equivalent of equations. The following examples illustrate this method of thinking. Example 1 Try to determine the positional relationship between the straight line l:Ax+By+C=0 and the ellipse C:x~2/a~2+y~2/b~2=1. The solution line l intersects the ellipse C and is tangent to the line. Separated, divided