Question

在X轴上求一点P,使P点到A点(-2,5)和B点(6,-4)的距离相等

Answer 1

P(x,y),|PA|=|PB|

|PA|=√(x+2)²+(y-5)²

|PB|=√(x-6)²+(y+4)²

(x+2)²+(y-5)²=(x-6)²+(y+4)²

x²+4x+4+y²-10y+25=x²-12x+36+y²+8y+16

16x-18y-23=o,

即,P点在直线16x-18y-23=o上.

如果,P点还在X轴上,说明了y=0,把y=0代入直线16x-18y-23=o,得到,X=23/16

设P（X,0）用两点间的距离公式,求出X