PS
# Region.m4
# https://tex.stackexchange.com/questions/606088/how-can-i-plot-in-latex
gen_init

 grsize = 3.3
 maxaxis = 4.5
 define Grid { (($1+maxaxis)/(2*maxaxis)*grsize-grsize/2,\
                ($2+maxaxis)/(2*maxaxis)*grsize-grsize/2) }

thinlines_
 box wid grsize ht grsize with .c at (0,0)
 tic = 0.05
 for x=-maxaxis to maxaxis by 0.5 do {
   line up tic from Grid(x,-maxaxis)
   y = abs(x)
   { if y/2 == int(y/2+0.5) then { sprintf("%g",x) at last line.start below } }
   line down tic from Grid(x,maxaxis)
   line right tic from Grid(-maxaxis,x)
   { if y/2 == int(y/2+0.5) then { sprintf("%g",x) at last line.start rjust } }
   line left tic from Grid(maxaxis,x)
   }
thicklines_

 n = 10
 ylim = 3
 for i=0 to n do { y = i/n*ylim
   P[i]: Grid(sqrt(1+y^2),y)
   P[-i]:( P[i].x,-P[i].y)
   Q[i]: (-P[i].x, P[i].y)
   Q[-i]:(-P[i].x,-P[i].y) }
 rgbfill(0.6,0.6,0.8,
   fitcurve(P,n,,-n)
   line to (P[n].x,P[n].x) then to (Q[-n].x,Q[-n].x) then to Q[-n]
   fitcurve(Q,n,,-n)
   line to (Q[n].x,-Q[n].x) then to (P[-n].x,-P[-n].x) then to P[-n] )

PE

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