How can I plot just one line of the hyperbola? Can somebdoy help me with fsolve?

This is my main code. I want to plot just the 3 lines of the hyperbola, the ones they are intersecting (Xt,Yt). Ho can I do it?

    Xt=randi([-10 10],1,1);

    Yt=randi([-10 10],1,1);

    [Xtx, Ytx] = meshgrid(-40:1:40, -40:1:40);

    R = Xtx + j*Ytx;

    for i = 1:3

        X(i)=randi([-10 10],1,1);
        Y(i)=randi([-10 10],1,1);
        x=[X(i) Xt];
        y=[Y(i) Yt];
        D(i)=sqrt((Xt-X(i))^2+(Yt-Y(i))^2);
        figure(1)
        line(x,y,'LineWidth',2);
        hold on;
        axis equal;
        plot(x,y,'*',Xt,Yt,'s');

    end

    Delay1=D(2)-D(1);

    Delay2=D(3)-D(1);

    D1P = abs(R-(X(1)+j*Y(1)));

    D2P = abs(R-(X(2)+j*Y(2)));

    D3P = abs(R-(X(3)+j*Y(3)));

    figure (1);

    contour(Xtx,Ytx,D1P-D2P,[0 0]);

    contour(Xtx,Ytx,abs(D1P-D2P));

    contour(Xtx,Ytx,D3P-D2P,[0 0]);

    contour(Xtx,Ytx,abs(D3P-D2P));

    % for m=1:3
    %     DP(m)=abs(R-(X(m)+j*Y(m)));
    %     figure(1);
    %     contour(Xtx,Ytx,DP(m)-DP(m+1));
    % end

    Xtt=-10;

    x0=[0;0];% Make a starting guess at the solution

    options = optimoptions('fsolve','Display','iter'); % Option to display output

    [x,fval]=fsolve(@position(Y,X,Delay1,Delay2);x0;options); % Call solver

I also want to generate a for loop with DP but it gives me an error with size of matrix I need some help also in these lines of the code.

Now i want to call this function with fsolve:

    function P=position(Y,X,Delay1,Delay2)

    X0=X(1);

    X1=X(2);

    X2=X(3);

    Y0=Y(1);

    Y1=Y(2);

    Y2=Y(3);

    Xt=-10:10;

    Yt=-10:10;

    P=[(Delay1)-sqrt((Xtxx-X1).^2+(Ytxx-Y1).^2)+sqrt((Xtxx-X0).^2+(Ytxx-Y0).^2); (Delay2)-sqrt((Xtxx-X2).^2+(Ytxx-Y2).^2)+sqrt((Xtxx-X0).^2+(Ytxx-Y0).^2)];

    end

I have an bracket error with the fsolve. My output of the funcion are (Xtxx,Ytxx). Need help in this.

Than you.

Answer 1

[Walter Roberson]

I think possibly you want

[x,fval] = fsolve(@(txx) position(txx, Y,X,Delay1,Delay2);x0;options); % Call solver

with

    function P = position(txx, Y,X,Delay1,Delay2)

    Xtxx = txx(1);
    Ytxx = txx(2);

    X0=X(1);
    X1=X(2);
    X2=X(3);
    Y0=Y(1);
    Y1=Y(2);
    Y2=Y(3);
    Xt=-10:10;
    Yt=-10:10;

    P=[(Delay1)-sqrt((Xtxx-X1).^2+(Ytxx-Y1).^2)+sqrt((Xtxx-X0).^2+(Ytxx-Y0).^2); (Delay2)-sqrt((Xtxx-X2).^2+(Ytxx-Y2).^2)+sqrt((Xtxx-X0).^2+(Ytxx-Y0).^2)];

    end

[Dayal Kewalramani]

Thank you Walter Roberson, you helped me a lot! Really grateful!