已知抛物线C:y^2=4x,A(x1,y1),B(X2,y2),D(x3,Y3)是C上除原点外的三点,且|AF|,|BF|,|DF|成等差数列,当AD的垂直平分线与X轴交于点E(3,0)时,求点B的坐标

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/12 10:07:19
已知抛物线C:y^2=4x,A(x1,y1),B(X2,y2),D(x3,Y3)是C上除原点外的三点,且|AF|,|BF|,|DF|成等差数列,当AD的垂直平分线与X轴交于点E(3,0)时,求点B的坐标

已知抛物线C:y^2=4x,A(x1,y1),B(X2,y2),D(x3,Y3)是C上除原点外的三点,且|AF|,|BF|,|DF|成等差数列,当AD的垂直平分线与X轴交于点E(3,0)时,求点B的坐标
已知抛物线C:y^2=4x,A(x1,y1),B(X2,y2),D(x3,Y3)是C上除原点外的三点,且|AF|,|BF|,|DF|成等差数列,
当AD的垂直平分线与X轴交于点E(3,0)时,求点B的坐标

已知抛物线C:y^2=4x,A(x1,y1),B(X2,y2),D(x3,Y3)是C上除原点外的三点,且|AF|,|BF|,|DF|成等差数列,当AD的垂直平分线与X轴交于点E(3,0)时,求点B的坐标
AD的垂直平分线与X轴交于点E(3,0)时 AE = DE
(x1 - 3)^2 + y1^2 = (x3 - 3)^2 + y3^2
==== (x1-x3)(x1+x3 - 2) = 0 ==== x1 + x3 = 2\
|AF|,|BF|,|DF|成等差数列,
则,x2 = (x1+ x3) /2 = 1
y2 = 2 ,- 2
B坐标是(1,2)或(1,-2)