A . MATHS - 直線

2008-03-27 5:02 am

1) 一直線通過L1 : 3x - 2y - 2 = 0 與L2 : 4x - 3y + 2 = 0 的交點。若點(1 , 4) 在該直線上 , 試求該直線的方程。

2) 試求通過兩直線2x + y - 4 = 0 與 2x - 3y = 0 的交點 , 且垂直於y軸的直線方程。

回答 (1)

Gabriella Montez

2008-03-27 5:09 am

✔ 最佳答案

1) Family of straight lines:
3x - 2y - 2 + k ( 4x - 3y + 2 ) = 0 where k is real
Sub ( 1 , 4 ),
3(1) -2(4) -2 + k [ 4(1) - 3(4) + 2 ] = 0
-7 - 6k = 0
k = -7 / 6
So the equation:
3x - 2y - 2 + ( - 7 / 6 )( 4x - 3y + 2 ) = 0
10x - 9y + 26 = 0
2) Family of straight lines:
2x + y - 4 + k ( 2x - 3y ) = 0 where k is real
Rearranging,
( 2 + 2k )x + ( 1 - 3k )y - 4 = 0
For the equation prependicular to the y - axis, it has slope = 0, i.e.
- ( 2 + 2k ) / ( 1 - 3k ) = 0
k = -1
Then the equation:
( 2 - 2 )x + ( 1 + 3 )y - 4 = 0
y - 1 = 0

參考: My Maths Knowledge

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