@acer  You wrote  "And how about requesting their spacing evenly by arclength rather than by value of the independent parameter? "

See the post  https://www.mapleprimes.com/posts/213452-Uniform-Point-Plot  with a procedure for this. 

@Carl Love  Sorry, but it seems to me that for a beginner, your method will be difficult to understand.

Another way for the same:

plots:-display(plot(sin(x), x= -Pi..Pi), plot(sin(x),x= -Pi..Pi, style=point, symbol= box, numpoints= 16, adaptive= false));

We can write very short for more symbols:

plot(sin(x), x= -Pi..Pi, style=pointline, symbol= box, numpoints= 30, adaptive= false);

@ecterrab  OP wants to plot the equation  |z+1|*|z-1|=1  (he mistakenly calls it a function), not independent graphs of the left and right sides of this equation.

@abdulganiy  Use the plots:-textplot  command.

@JAMET You have to do it yourself. It's quite easy if you first study the solutions I've shown.

@AHSAN  See my updated answer.

@janhardo I think it is useful to know the physical meaning of this curvilinear integral: if  2*x+y^2  is the linear density at the point  (x,y) of the segment, then the value of the integral is the mass of this segment. 

@Preben Alsholm  Thank you for the improvement.

@ActiveUser  See the corrected answer.

You have already built it. cos(Pi/4)  is a constant. And what is the question?

@Scot Gould You're right. Using  add  instead of  sum  avoids many problems. 

@sunit  You are not required to apply the command to every equation. Build a system and apply the command to this system as in the example:

convert({1.0*x+0.3*y=1,2*x-1.0*y=3}, rational);

@nguyenhuyenag 

This is also written in the help.

Solution for your example:

restart;
bl:=sqrt(2)-1>0:
evalb(evalf(bl));

                               true

@Carl Love  Thanks. The  seq  is my favorite command in Maple. Owners of older versions of Maple (< Maple 13 or 14) , who do not know about  zip ,  can simply write this:

A:=[1,2,3]:
B:=[7,8,9]:
[seq(f(A[i],B[i]),i=1..nops(A))];

The  seq  command can completely replace map, zip, and ~  (which of course make the code a little shorter).

Here's another animation in which the ellipse of a given shape (defined by the parameter  k ) rotates around a given triangle:

Edit.

Download ells2.mw