众所周知,在解析几何中,直线与椭圆位置关系的判断,常选择代数法和几何法.设直线l的方程为:Ax+By+C=0(A~2+B~2≠0),椭圆E的方程为:x~2/a~2+y~2/b~2=1(a>b>0).代数法即是联立方程Ax+By+C=0和x~2/a~2+y~2/b~2=1,消去x或y利用判别式判断,当Δ=0时,直线与椭圆相切;当Δ>0时,直线与椭圆相交;当Δ<0时,直线与椭圆相离.而几何法是利用仿射变换将椭圆变为圆,比较圆心到直线的距离与圆的半径大小进行 As we all know, in analytical geometry, the relationship between the position of the line and the ellipse often choose algebra and geometry method. Let straight line equation l: Ax + By + C = 0 (A ~ 2 + B ~ 2 ≠ 0) The equation of E is: x ~ 2 / a ~ 2 + y ~ 2 / b ~ 2 = 1 (a> b> 0) Algebra method is the simultaneous equations Ax + By + C = 0 and x ~ 2 / a 2 + y ~ 2 / b ~ 2 = 1, eliminate x or y Judgments by discriminant, when Δ = 0, the line is tangent to the ellipse; when Δ> 0, the line intersects with the ellipse; when Δ <0 , The straight line is away from the ellipse, while the geometric method uses the affine transformation to transform the ellipse into a circle, and the distance between the circle center and the straight line is equal to the radius of the circle