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判断直线与椭圆位置关系的常规方法是将直线方程与椭圆方程联立消元,然后根据所得一元二次方程的根的情况来判断直线与椭圆的位置关系.这种方法的不足之处是运算量较大.在解客观题时,还有一种能快速判断直线与椭圆位置关系的方法.设直线l:Ax+By+C=0(A≠0且B≠0),椭圆E:
The conventional method of judging the relationship between a straight line and an ellipse is to determine the positional relationship between a straight line and an ellipse by combining the linear equation and the elliptic equation with the elimination unit, and then determine the position relationship between the straight line and the ellipse according to the obtained root of the unary quadratic equation. The disadvantage of this method is the operation. Large amount. In solving the objective problem, there is a method that can quickly determine the relationship between the straight line and the ellipse. Let the line l: Ax+By+C=0 (A≠0 and B≠0), the ellipse E: