请问下面的三个方程求x,（x-xa)^2+(y-ya)^2=R1^2(x-xb)^2+(y-yb)^2=R2^2(x-xc)^2+(y-yc)^2=R3^2其中xa,ya,xb,yb,xc,yc和R1,R2,R3都已知,求x和y,

Question

请问下面的三个方程求x,
（x-xa)^2+(y-ya)^2=R1^2
(x-xb)^2+(y-yb)^2=R2^2
(x-xc)^2+(y-yc)^2=R3^2
其中xa,ya,xb,yb,xc,yc和R1,R2,R3都已知,求x和y,

Answer 1

用2式-1式：（2x-xb-xa）(xa-xb)+(2y-yb-ya)(ya-yb)=R2^2-R1^2；同理,
用3式-1式：（2x-xc-xa）(xa-xc)+(2y-yc-ya)(ya-yc)=R3^2-R1^2；整理得：
2(xa-xb)x+2(ya-yb)y+xb^2-xa^2+yb^2-ya^2=R2^2-R1^2；
2(xa-xc)x+2(ya-yc)y+xc^2-xa^2+yc^2-ya^2=R3^2-R1^2；
此时变成二元一次方程,自己解答吧,仔细一点就ok啦!