Individua cosa rappresenta nello spazio (x,y,z) l'equazione:  (x−z)² + (y−z)² = 0.

L'intersezione tra il piano x = z e il piano y = z, ossia la retta x = y = z.

La figura col software online WolframAlpha:

3d plot z=x, x=-3..3, y=-3..3, z=-3..3, view from (5,5,5)
3d plot z=y, x=-3..3, y=-3..3, z=-3..3, view from (5,5,5)

# Come è stata tracciata la figura seguente
x <- y <- z1 <- c(-1.2,1.2)
z <- array(rep(z1[1],4), dim=c(2,2)); th <- 50; ph <- 15
F <- persp(x,y,z,theta=th,phi=ph, scale=FALSE, zlim=z1,xlim=x,ylim=y,
             ticktype="detailed",nticks=3,d=5)
figura <- function(F) {
   lines(trans3d(c(0,0),c(0,0),c(0,z1[2]),pmat=F),col="red")
   lines(trans3d(c(0,x[2]),c(0,0),c(0,0),pmat=F),col="red")
   lines(trans3d(c(0,0),c(0,y[2]),c(0,0),pmat=F),col="red")
   lines(trans3d(c(0,0),c(0,0),c(z1[1],0),pmat=F),col="red",lty=3)
   lines(trans3d(c(x[1],0),c(0,0),c(0,0),pmat=F),col="red",lty=3)
   lines(trans3d(c(0,0),c(y[1],0),c(0,0),pmat=F),col="red",lty=3)}
m <- 1.19
for(j in (-20:20)/20*m) for(i in (-30:30)/30*m)
         points(trans3d(i,j,i,pmat=F),col="green",pch=".",cex=1)
for(j in (-20:20)/20*m) for(i in (-30:30)/30*m)
         points(trans3d(j,i,i,pmat=F),col="orange",pch=".",cex=1)
for (i in (-90:90)/90*m) points(trans3d(i,i,i,pmat=F),col="blue",pch=".",cex=2)
figura(F)