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f4maths equation of straight line ?
find the equations of straight lines passing through （4，2）and the area bounded by the line,the x-axis and the y-axis is 18 square units.
1 Answer
- 老怪物Lv 72 weeks agoFavorite Answer
設斜率是 m.
m 存在 且 m≠ 0 直線與兩軸才都能相交.
則方程式
y-2 = m(x-4)
則
x-截距 = 4+(-2)/m = 4-2/m
y-截距 = 2 + m(-4) = 2-4m
則: 由此直線與兩軸構成的三角形面積
18 = (1/2)．|4-2/m|．|2-4m|
若 m < 0 則得
18 = (1/2)(4-2/m)(2-4m)
= 4+4-8m-2/m
= 8 - 8m - 2/m
即 8m+2/m+1o = 0.
解之, 得 m = -1/4 or -1.
直線為 x + 4y = 12 或 x + y = 6.
若 m > 0, 則 m ≠ 1/2, 且
m < 1/2 時 4-2/m < 0, 2-4m > 0
m > 1/2 時 4-2/m > 0, 2-4m < 0
故
-18 = 8 - 8m - 2/m
即 8m + 2/m - 26 = 0
解之, 得 m = (13±3√17)/8
直線為
y = [(13±3√17)/8](x-4) + 2
