Ellipse in parametric form ?

I'm trying to create an ellipse in parametric form. I have just two Foci along the major axis. So, how shall I get r1, r2 etc.

   point1  = 10  8
    point2 = 25  20

The syntax is

t = linspace(0, 2*pi, 200);

xt = r1 * cos(t) + xc;

yt = r2 * sin(t) + yc;

cot = cos(theta); sit = sin(theta);

x = xt * cot - yt * sit;

y = xt * sit - yt * cot;

plot(x, y, '-');

[Ramesh Bala]

% or in other general forms :

% data

t = linspace(0,2*pi,80); % the domain of the parameter t.

x = @(t)r1.*cos(t); 

y = @(t)r2.*sin(t); 

figure(1)

ELLIPSE = plot(x(t),y(t));

hold off

Answer 1

[Matt J]

You cannot determine the ellipse with only the foci. You also need to know r1. Once you know that however, you can determine r2 readily,

xc_yc=(point1+point2)/2;
c=norm(point1-xc_yc);
r2 = r1^2-c^2;

See also Ellipse in Cartesian coordinates.

[Ramesh Bala]

Danke ! how to get that r1. I think r1 = 2a ? major axis length so how to get a from foci (xy ) coords??

[Matt J]

The major axis length needs to be given. You cannot derive it from the foci. Two different ellipses with different major axis lengths can have the same foci.

[Ramesh Bala]

Alright ! Lemme have a check

Thanks for the answer.

[Ramesh Bala]

I couldn't get the proper work out for this. Could you share any code regarding this case

[Matt J]

I already told you that it was impossible. The foci alone aren't enough.

[Ramesh Bala]

yeah I know that ,I thought to take the surrounding rectangle boundary as tangent and then to draw an ellipse ?