Here’s the content of the script I will use with gnuplot to make a graph of a circle using Cartesian coordinates. Save the file as ‘circle.gpt’ and run as a script with command ‘gnuplot circle.gpt’. Alternatively you could write the commands in gnuplot using the interactive mode.

set terminal png
set nokey
set xrange[-10:10]
set yrange[-10:10]
set output "circle.png"
set samples 100000
r = 5.0 ## radius
a = 3.0 ## x shift
b = 4.0 ## y shift
f1(x) = sqrt(r**2 - (x-a)**2) - b
f2(x) = sqrt(r**2 - (x-a)**2) + b
plot f1(x) lw 3, -1*f2(x) lw 3 lt 1