標題: LOCUS [打印本頁] 作者: ting 時間: 10/8/2007 08:41 PM 標題: LOCUS 整課的EXERCISE都做了 剩這不懂@.@
A line passing through the point (1,0) cut the curves y^2=4x at two points A and B. Find the equation of locus of the mid point P of AB as the line moves
LET了N 個VARIABLES...計不到作者: sapphire 時間: 10/8/2007 09:41 PM Let the line be y=mx+c The line pass through (1,0). Put (1,0) into the eqt. 0=m+c m=-c ∴The eqt becomes y=m(x-1)
put y=m(x-1) into y^2=4x (m^2)(x-1)^2=4x (mx)^2-2(m^2+2)x+A^2=0 ------(1)
Let the mid-pt P be (x1,y1) x1=sum of roots of (1) * 1/2=(m^2+2)/m^2