题目

如图,A(0,3),B(-1,0),点C在双曲线Y=K/X上(x

提问时间：2021-05-06

答案

设C点坐标(x3, y3), 则
D点坐标(x3/2, (y3+3)/2)
C,D都在Y=k/x上,
y3 = k/x3
(y3+3)/2 = k/(x3/2)
所以
x3y3 = k,
4k = x3y3 +3x3
得k = x3
y3 = 1
因为BC垂直AB, 这两段直线,斜率乘积= -1
(y3-0)/(x3-(-1)) * (3-0)/(0-(-1)) = -1
所以 3y3 +(x3 +1) =0
x3 = -(3y3 +1) = -4
所以 k = x3 = -4