1) Consider thetwo straight lines L(1) : x+2y+3=0 and L(2) : ax+by-2=0, Suggest two pairs of possible values fora and b, and describe how to find the relationship between a and b , if
(a) L(1)//L(2)
(b)L(1)perpendicular L(2)2) Consider thetwo straight lines L(1): kx+8y+5=0 and L(2):9x-6y+5=0(a) Explainwhy L(1) and L(2) must not be coincident.(b) If L(1)and L(2) do not intersect, find the value of k.3) In the figure,there are three straight lines L(1),L(2) and L(3), where L(1)perpendicular L(2)and L(2)parallel L(3). L(1) cuts L(2) at a point P on the x-axis, and cuts L(3)at a point Q. The y-intercept of L(2) and L(3) are -4 and 0 respectively, andthe slop of L(1) is -2(a) Find theequations of L(1),L(2) and L(3)(b) Find the lengthof PQ, correct to 3 significant figures. Thank you *-* answer thequestion in complete step …!!!!!!!!!
F4 Equation of Staright Lines
2012-02-11 3:39 am
回答 (1)
2012-02-11 6:42 pm
✔ 最佳答案
1.(a)
Slope of L1 = -1/2
Slope of L2 = -a/b
L1//L2
(Slope of L1) = (Slope of L2)
-1/2 = -a/b
b = 2a
When a = 2, b = 4
When a = 3, b = 6
(b)
L1⊥L2
(Slope of L1) x (Slope of L2) = -1
(-1/2) x (-a/b) = -1
a/2b = -1
a = -2b
When a = 2, b = -1
When a = -2, b = 1
=====
2)
Put x = 0 into L1 :
0 + 8y + 5 = 0
y = -5/8
The y-intercept of L1 = -5/8
Put x = 0 into L2 :
0 - 6y + 5 = 0
y = 5/6
The y-intercept of L2 = 5/6
Since L1 and L2 have differencey-intercepts, they must NOT be coincident.
(b)
If L1 and L2 do not intersect, they must be parallel.
Slope of L1 = Slope of L2
-k/8 = -9/(-6)
-k/8 = 3/2
-2k = 24
k = -12
=====
3)
(a)
Slope of L1 = -2
L1⊥L2
Hence, slope of L2 = -1/(-2) = 1/2
L2 passes through (0, -4) and with a slope 1/2.
L2 : y + 4 = (1/2)(x - 0)
L2 : 2y + 8 = x
L2 : x - 2y - 8 = 0
Put y = 0 into L2 :
x - 0 - 8 = 0
x = 8
P = (8, 0)
L1 passes through P(8, 0) and with a slope -2.
L1 : y - 0 = -2(x - 8)
L1 : y = -2x + 16
L1 : 2x + y - 16 = 0
L2 // L3
Slope of L3 = Slope of L2 = 1/2
L3 passes through (0, 0) and with a slope 1/2.
L3 : y - 0 = (1/2)(x - 0)
L3 : 2y = x
L3 : x - 2y = 0
(b)
L1 : 2x + y - 16 = 0 ...... [1]
L3 : x - 2y = 0 ...... [2]
From [2] :
x = 2y ...... [3]
Put [3] into [1] :
2(2y) + y - 16 = 0
5y = 16
y = 3.2
Put y = 3.2 into [3]
x = 2(3.2)
x = 6.4
Hence, Q = (6.4, 3.2)
PQ
= √[(8 - 6.4)² + (0 - 3.2)²]
= √(1.6² + 3.2²)
= 3.58 units (to 3 sig. fig.)
參考: 土扁
收錄日期: 2021-04-13 18:32:01
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