Question

求曲线xy-y-1=0关于直线x+y-5=0对称的曲线的方程

Answer 1

设点(x0,y0)为xy-y-1=0上一点,

关于直线x+y-5=0对称的点是:(a,b)

(y0-b)/(x0-a)=1

(x0+a)/2+(y0+b)/2-5=0

联立解得

a=5-y0,b=5-x0

代入

xy-y-1=0

(5-y0)(5-x0)-(5-x0)-1=0

化简是:

4x0+5y0-x0y0-19=0

所求的方程是:

4x+5y-xy-19=0