作业帮直线的倾斜角与斜率 例1、例2
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/28 18:12:23
直线的倾斜角与斜率 例1、例2
|k| < 1,-1 < k = tanα < 1
0 ≤ k < 1:0 ≤ α < π/4
-1 < k < 0:3π/4 < α < π
系数成比例(但不与常数项成比例)时, 二者平行:
1 :2m = 1 + m :4
m² + m - 2 = (m + 2)(m - 1) = 0
m = -2: 此时二直线均可变为x - y = 4, 舍去m = -2
m = 1: 此时二直线平行
二者可分别变为y = -x/(1 + m) + (2 - m)/(1 + m)和y = -mx/2 - 4,斜率分别为-1/(1 + m),-m/2
其积为[-1/(1 + m)](-m/2) = -1
m = -2/3
m≠ -2且m ≠ 1时,二者相交
0 ≤ k < 1:0 ≤ α < π/4
-1 < k < 0:3π/4 < α < π
系数成比例(但不与常数项成比例)时, 二者平行:
1 :2m = 1 + m :4
m² + m - 2 = (m + 2)(m - 1) = 0
m = -2: 此时二直线均可变为x - y = 4, 舍去m = -2
m = 1: 此时二直线平行
二者可分别变为y = -x/(1 + m) + (2 - m)/(1 + m)和y = -mx/2 - 4,斜率分别为-1/(1 + m),-m/2
其积为[-1/(1 + m)](-m/2) = -1
m = -2/3
m≠ -2且m ≠ 1时,二者相交