Plotting ellipses with parametric curves
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Szabolcs Simon-Guth
on 9 Nov 2021
Commented: Szabolcs Simon-Guth
on 9 Nov 2021
Hi all!
I need to plot the following ellipses on the same plot:
Ellips 1: ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795159/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795159/image.png)
Ellipse 2: ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795164/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795164/image.png)
I have substituted the formula for the second ellipse by u and v:
u = ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795169/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795169/image.png)
v = ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795174/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795174/image.png)
Ellipse 2: ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795179/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795179/image.png)
I have used the following parametrisation:
For an ellipse with the general fomula ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795184/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795184/image.png)
the parametrization:
and ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795194/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795189/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795194/image.png)
So, I have rearranged the equation of both ellipses to fit the general formula and then calculated a and b according the get the parametrization above. I was supposed to get the following plot:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795199/image.png)
Instead I have got this:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/795204/image.png)
I have written the following code:
% First ellipse
t = linspace(0,2*pi,200);
a = sqrt(2);
b = sqrt(2/3);
x = a.*cos(t);
y = b.*sin(t);
plot(((1/2)*(x.^2)), ((3/2).*(y.^2)), '-k', 'LineWidth', 1.5)
axis equal
hold on
% Second ellipse
t = linspace(0,2*pi,200);
a = 2;
b = 1;
x = (-a/3).*(cos(t)+((-2*b/3).*sin(t)));
y = (((2*a/3).*cos(t))+((7*b/3).*sin(t)));
u = x-(2.*y);
v = (2.*x)+y;
plot(((1/4).*(u.^2)), ((v.^2)), '-k', 'LineWidth', 1.5)
axis equal
hold off
What is it that I'm doing wrong? I am very thankful for all the help in advance!
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Accepted Answer
Chunru
on 9 Nov 2021
% First ellipse
t = linspace(0,2*pi,200);
a = sqrt(2);
b = sqrt(2/3);
x = a.*cos(t);
y = b.*sin(t);
%plot(((1/2)*(x.^2)), ((3/2).*(y.^2)), '-k', 'LineWidth', 1.5)
plot(x, y, '-k', 'LineWidth', 1.5)
axis equal
hold on
% Second ellipse
t = linspace(0,2*pi,200);
a = 2;
b = 1;
u = a.*cos(t);
v = b.*sin(t);
xy= ([1 -2; 2 1])\[u; v]; % since [u; v] = [1 -2; 2 1][x; y]
x = xy(1, :);
y = xy(2, :);
%plot(((1/4).*(u.^2)), ((v.^2)), '-g', 'LineWidth', 1.5)
plot(x, y, '-g', 'LineWidth', 1.5)
axis equal
hold off
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