code for diagram

> f:=sqrt((x+5)^2+y^2)+sqrt(x^2+(y+5)^2)=20:
PP:=[6,fsolve(subs(x=6,f),y)]:
AA:=[-5,0]:BB:=[0,-5]:
lines:=plot({[AA,PP],[BB,PP],[AA,BB]},linestyle=3,
thickness=2,color=blue):
elps:=plots[implicitplot](f,x=-15..15,y=-20..20,
thickness=3,color=red):
txt:=plots[textplot]({[-6,-1,`A`],[.5,-5.7,`B`],[PP[1]+1,PP[2]+.5,`P`,`P`]},font=[TIMES,BOLD,24]):
dsk1:=plottools[disk](AA,.2,style=patch,color=black):
dsk2:=plottools[disk](BB,.2,style=patch,color=black):
dsk3:=plottools[disk](PP,.2,style=patch,color=black):
plots[display]({elps,lines,txt,dsk1,dsk2,dsk3},
xtickmarks=[5,0,-5,-10],ytickmarks=[-15,-10,-5,0,5],
axesfont=[TIMES,BOLD,18],labels=[` `,` `]);