# Using the ellipse graph.

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John Lutz on 30 Sep 2017
Answered: Ali Nafar on 13 Jun 2019
In polar coordinates (r,t), the equation of an ellipse with one of its foci at the origin is r(t) = a(1 - e2)/(1 - (e)cos(t)) I'm confused how to set this up, as I have never occurred an ellipse graph before. where a is the size of the semi-major axis (along the x-axis) and e is the eccentricity. Plot ellipses using this formula, ensuring that the curves are smooth by selecting an appropriate number of points in the angular (t) coordinate Thank you.
function untitled3
a = 1/2(b);
e = 0.5;
t = linspace(0,2*pi);
r = a(1 - e.^2)./(1 - (e)*cos(t));
plot(r,t)
axis equal
end

Image Analyst on 30 Sep 2017
You need to define b using a and e, not assume b is already defined like you did.
John Lutz on 30 Sep 2017
Still does not work, really confused on this.
t = linspace(0,2*pi);
e = 2*pi;
a = 1/2.*(2*pi);
r = (a.*(1 - e.^2) ./ (1 - ((e)*cos(t))));
axis equal
plot(r,t);
also this doesn't work either, tried many times to get this to work but it doesn't.

Henry Giddens on 30 Sep 2017
Your equation ends up with some negative values - (which I'm not sure can be correct?), but if you are using polar coordinates, then use the polarplot or polar commands:
polarplot(t,abs(r))

Ali Nafar on 13 Jun 2019
L=0.5;
e=0.5;
phi0=0;
phi=linspace(0,2*pi);
rho=L*(1-e^2)./(1-e*cos(phi-phi0));
polar(phi,rho)