直線L1:4x+y-6=0與通過P(5,3)的直線L互相垂直。
a.求L的斜率。
b.求L的方程。
c.求L和L1的交點坐標
http://img835.imageshack.us/img835/9044/123456sy.png
F.5直線方程......
2010-09-20 4:14 am
回答 (2)
2010-09-20 4:29 am
✔ 最佳答案
(a) L1的斜率 = -4L⊥L1
L的斜率 x L1的斜率 = -1
L的斜率 = -1/(-4)
L的斜率 = 1/4
(b) L的方程:
y - 3 = 1/4(x-5)
y = x/4 + 7/4
(c) L1 : 4x+y-6 = 0 ---(1)
L : y = x/4 + 7/4 ---(2)
考慮(1), y = 6 - 4x ---(3)
代入(3)於(2),
6-4x = x/4 + 7/4
24-16x = x+7
17x = 17
x = 1
代入x = 1 於(3),
y = 6-4(1) = 2
L和L1的交點是(1,2)
參考: Knowledge is power.
2010-09-20 4:25 am
a)
L的斜率 x L1的斜率 = -1
L1的斜率 : y = -4x + 6 , -4
L的斜率 = -1/-4 = 1/4
b)
y = mx + c
3 = 5/4 + c
c = 7/4
L:y = x/4 + 7/4
L:x - 4y + 7 = 0
c)
4x + y - 6 = 0 ... (1)
x - 4y + 7 = 0 ... (2)
(2), 4x - 16y + 28 = 0
(1) - (2),
17y - 34 = 0
y = 2
So, 4x - 16y + 28 = 0
x = (-28 + 16*2) = 4/4 = 1
So, 交點坐標(1,2)
L的斜率 x L1的斜率 = -1
L1的斜率 : y = -4x + 6 , -4
L的斜率 = -1/-4 = 1/4
b)
y = mx + c
3 = 5/4 + c
c = 7/4
L:y = x/4 + 7/4
L:x - 4y + 7 = 0
c)
4x + y - 6 = 0 ... (1)
x - 4y + 7 = 0 ... (2)
(2), 4x - 16y + 28 = 0
(1) - (2),
17y - 34 = 0
y = 2
So, 4x - 16y + 28 = 0
x = (-28 + 16*2) = 4/4 = 1
So, 交點坐標(1,2)
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