# How to plot circle by one single equation?

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Ameer Hamza on 13 May 2018
I need code which plot the circle in one single equation (variable). I have the code but i need code of single equation, the code which i have, it is composed of two equations as follow :
r=2;
x=0;
y=0;
th = 0:pi/6:2*pi;
xunit = r * cos(th) + x;
yunit = r * sin(th) + y;
plot(xunit, yunit);

John D'Errico on 13 May 2018
Edited: John D'Errico on 13 May 2018
As one "equation" what does that mean? About the best I can offer is this:
r=2;
x0=0;
y0=0;
ezplot(@(x,y) (x-x0).^2 + (y-y0).^2 -r^2)
axis equal
Be careful that the units are equal for the two axes, else it ill not look circular.
I could also have done it using fimplicit.
r=2;
x0=0;
y0=0;
syms x y
fimplicit((x-x0).^2 + (y-y0).^2 -r^2)
axis equal
So, in either case, only one equation.
If you really insist on only one "variable, then you need to use a polar coordinate transformation. Thus, you can do it in terms of polar angle theta, as:
r=2;
x0=0;
y0=0;
theta = linspace(0,2*pi,100);
plot(x0 + r*cos(theta),y0 + r*sin(theta),'-')
axis equal
So only one variable, theta. If you are hoping for something else, something more or less, then you need to explain carefully what the goal is here.
Are you looking for a simple way to plot a circle? Perhaps try this:
cplot = @(r,x0,y0) plot(x0 + r*cos(linspace(0,2*pi)),y0 + r*sin(linspace(0,2*pi)),'-')
Now you have a little function that will plot a circle.
cplot(2,0,0)
hold on
cplot(3,1,2)
cplot(1,-1,1)
axis equal

#### 1 Comment

Abdulrahman Saad on 5 Oct 2019
Thank you very much

Aditya Gupta on 26 Jun 2020
originX = 0;
originY = 0;
'Curvature',[1 1]);
axis equal