Question

点P(x,y)在圆x^2＋y^2－2x－2y＋1＝0上 则（x+1）/(y+1)的最小值

Answer 1

圆方程:x²+y²-2x-2y+1=0

(x²-2x+1)+(y²-2y+1)=1

(x-1)²+(y-1)²=1

设x-1=cosa,y-1=sina

(x+1)/(y+1)=(2+cosa)/(2+sina)

显然当cosa=0,sina=1时取最小值(2+0)/(2+1)=2/3