Question

已知经过点P(2,0),斜率为4/3的直线和抛物线y的平方等于2x相交于A,B

已知经过点P(2,0),斜率为4/3的直线和抛物线y的平方等于2x相交于A,BAB的中点为M求M的坐标用 参数方程解决这道题 不要用联立方程!!! 学霸帮忙啊

Answer 1

过点P(2,0),斜率为4/3的直线
y-0 =(4/3)(x-2)
3y= 4x-8
4x-3y-8=0 (1)
抛物线 : y^2=2x (2)
A(x1,y1) , B(x2,y2), M=( (x1+x2)/2 , (y1+y2)/2 )
sub (1) into (2)
[(4x-8)/3]^2 =2x
(4x-8)^2 =18x
16x^2-64x+64 =18x
16x^2-82x+64 =0
8x^2-41x+32 =0
x1+x2 = 41/8
(x1+x2)/2 = 41/16
from (1)
4x-3y-8=0
4x1-3y1-8=0 (3)
4x2-3y2-8=0 (4)
(3)+(4)
4(x1+x2) -3(y1+y2) =16
4(41/8) -3(y1+y2) =16
(y1+y2) = 3/2
(y1+y2)/2 =3/4
M=( (x1+x2)/2 , (y1+y2)/2 )=( 41/16 , 3/4 )

追问

不要联立方程