Solve 2 quadratic equations

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avinash desh
avinash desh 2015-11-11
评论： Walter Roberson 2015-11-12
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.

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Rajan Chauhan
Rajan Chauhan 2015-11-11
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
  2 个评论
avinash desh
avinash desh 2015-11-11
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
Rajan Chauhan 2015-11-12
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')

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更多回答（1 个）

Walter Roberson
Walter Roberson 2015-11-12
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;
  2 个评论
avinash desh
avinash desh 2015-11-12
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
Walter Roberson 2015-11-12
The first answer would be x=xc1, y=yc1

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