有關Amaths的直線族問題

首先我地先prove左existance part先
http://i299.photobucket.com/albums/mm309/lokwanshan/ScreenHunter_06Jun060053.gif

所以條式係可以通過個interception point
但係...係咪所有既線都可以用條式表示呢
定係條式淨係可以show到某幾條既線呢
跟住我地就prove下
http://i299.photobucket.com/albums/mm309/lokwanshan/ScreenHunter_07Jun060104.gif
由此可以知道
所有線都satisfy果條式

2008-06-06 04:21:46 補充：
L係代表Ax+By+C
L^2=(Ax+By+C)^2
=A^2x^2+B^2y^2+2ABxy+......
當然唔係直線啦
L^2係conics,即係parabola,ellipse果d
而係邊種就要睇返ABC係咩喇~

Let the two lines be L=0 and M=0. The intersecting point will satisfy L= 0 and will satisfy M = 0 individually, therefore, it will also satisfy L +kM = 0 for any values of k. Therefore, L +kM= 0 will be the family of straight lines passing through the intersecting point.

2008-06-02 16:11:07 補充：
Since k is a number (positive or negative), L + kM = 0 is still an equation of a straight line.

2008-06-02 16:20:38 補充：
You can argue why the family is L +kM = 0 and not L^2 +kM = 0 or L^2 +kM^2 = 0 etc. since the intersecting point also satisfies them. This is because only L +kM = 0 is a straight line, others are not straight lines.