a-maths~~~~~

2007-10-27 6:55 pm
一條斜率為m的直線通過C(-2,3)並與曲線y=1/2 (x+1)²相交於P和Q。若C是PQ的中點,求m的值和該直線方程。

回答 (1)

2007-10-27 7:48 pm
✔ 最佳答案
let L : y=mx+c

put it into the curve,
mx + c = 1/2 (x+1)²
mx + c = x²/2 + x + 1/2
x ² + 2x - 2mx +1 -2c =0………..(1)


let P=(x1,y1) Q=(x2,y2)
the x-coordinate of C = (x1+x2)/2
x1+x2= sum of root of (1)
the x-coordinate of C
= (x1+x2)/2
=(2m-2)/2
=m-1
m-1=-2
m=-1

put C(-2.3) in to y=-x+c,
3=2+c
c=1
L:y=-x+1



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