高等代数解析几何动点与两平面x+y-z=1x+y+z+1=0的距离的额平房和等于1则动点轨

Question

高等代数解析几何 动点与两平面x+y-z=1 x+y+z+1=0的距离的额平房和等于1 则动点轨

Answer 1

假设点（x,y,z）满足题意,那么：
d_1 ^2 +d_2 ^2
=(x+y-z-1) ^2 /3 + (x+y+z+1) ^2 /3
=(x+y-z-1) ^2 + (x+y+z+1) ^2 /3
=1
==>(x+y)^2 +(z+1)^2 =3/2为所求.