Question

已知直线y=x+1和双曲线y=k/x的两个交点为A(x1,y1),B(x2,y2),且x1x2+y1y2+4=0,则这个

Answer 1

y=x+1

y=k/x

x + 1 = k/x

x^2 + x - k = 0

x1x2 = -k

又

y=x+1 .x = y - 1

y=k/x .x = k/y

y - 1 = k/y

y^2 - y - k = 0

y1y2 = -k

代入 x1x2+y1y2+4=0.-k - k + 4 = 0

k = 2

所以这个反比例函数解析式为：y = 2/x