已知A(1,0),P,Q是圆x^2+y^2=5上的两个动点,AP⊥AQ,则PQ的最小值是() A.2 B.2√3 C.3√2 D.2√5
问题描述:
已知A(1,0),P,Q是圆x^2+y^2=5上的两个动点,AP⊥AQ,则PQ的最小值是() A.2 B.2√3 C.3√2 D.2√5
答
[y1/(x1-1)][y2/(x2-1)]=-1y1y2/[(x1-1)(x2-1)]=-1y1y2=-(x1-1)(x2-1)=-(x1x2-x1-x2+1) |PQ|=√[(y1-y2)²+(x1-x2)²]=√(y1²-2y1y2+y2²+x1²-2x1x2+x2²)=√(5-x1²+2x1x2-2x1-2x2+2...