Solve 2 quadratic equations

I have 2 quadratic equations with 2 known and 2 unknown. Ho do I write a script file to solve this equation. The equations are: (x1-xc)^2+(y1-yc)^2=R^2 (x2-xc)^2+(y2-yc)^2=R^2 I know the values for x1,x2,y1,y2 and R, these can be input manually in the script. I need to find xc and yc. How do I write a code to solve it in Matlab. Any help would be greatly appreciated.

Answer 1

[Rajan Chauhan]

    syms xc;
    syms yc;

    [x y] = solve('(x1-xc)^2+(y1-yc)^2=R^2 ,(x2-xc)^2+(y2-yc)^2=R^2')

put the values of R ,x1 and y1 in above equation you will get your answer hopefully

[avinash desh]

Hello, Thank you for the reply. I tried this and got the following error message ??? Undefined function or method 'syms' for input arguments of type 'char'.

Error in ==> myquadratic at 1 syms xc;

[Rajan Chauhan]

which version you are using ?? try this:

syms x y integer
[x y] = solve('(x1-xc)^2+(y1-yc)^2=R^2 ,(x2-xc)^2+(y2-yc)^2=R^2')

Answer 2

[Walter Roberson]

Undefined function or method 'syms' for input arguments of type 'char'.

indicates that either you do not have the Symbolic Toolbox licensed or you do not have it installed. If you have the Student Version then it includes a license for the Symbolic Toolbox, and you should install it and try again with

make your assignments to x1, y1, x2, y2 and R above this point

syms xc yc
[XC, YC] = solve((x1-xc)^2+(y1-yc)^2 - R^2, (x2-xc)^2+(y2-yc)^2 - R^2, xc, yc);

If you do not have the symbolic toolbox available then there are method involving the optimization toolbox and fsolve() . And if you do not have that toolbox then you can do things like

initialvals = rand(1,2);
XCYC = fminsearch( @(xyc) (x1-xyc(1))^2+(y1-xyc(2))^2 - R^2 + (x2-xyc(1))^2+(y2-xyc(2))^2 - R^2, initialvals);

Be careful: there are two solutions.

In code, with the two solutions being xc1, yc1 and xc2, yc2:

t1 = -y1 + y2;
t2 = (x1 - x2);
t3 = (t2 ^ 2);
t4 = (x1 ^ 2);
t6 = 2 * x2 * x1;
t7 = x2 ^ 2;
t8 = (y1 ^ 2);
t9 = (y1 * y2);
t10 = 2 * t9;
t11 = (y2 ^ 2);
t14 = (R ^ 2);
t18 = sqrt((t3 * (t4 - t6 + t7 + t8 - t10 + t11) * (4 * t14 - t4 + t6 - t7 - t8 + t10 - t11)));
t22 = -t1;
t23 = (t22 ^ 2);
t24 = t4 - t6 + t7 + t23;
t25 = t2 * (x1 + x2) * t24;
t27 = 1 / t2;
t29 = 1 / t24;
t31 = t8 * y1;
t32 = t8 * y2;
t36 = (-x2 + x1 - y2) * (-x2 + x1 + y2) * y1;
t37 = t11 * y2;
t38 = t3 * y2;
t45 = 1 / (2 * t8 - 4 * t9 + 2 * t11 + 2 * t3);
xc1 = (t1 * t18 + t25) * t27 * t29 / 2;
yc1 = (t31 - t32 + t36 + t37 + t38 + t18) * t45;
xc2 = (t18 * t22 + t25) * t27 * t29 / 2;
yc2 = (t31 - t32 + t36 + t37 + t38 - t18) * t45;

[avinash desh]

Hello Thank you for your suggestion. I do not have syms function in my version of Matlab. I tried the 2 solution code, when I run this I do not get an answer nor an error message. I have attached the code. Could you please let me know what's wrong in the code.

[Walter Roberson]

The first answer would be x=xc1, y=yc1