LOCUS

ting

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

sapphire

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

put x1 into y=m(x-1)
y1=2/m
m=2/(y1)

put m into x1, the required eqt. is y^2=2x-2