Using (x-a) ^ 2 + (y-b) ^ 2 = r ^ 2, the values ​​of a, b and r are known. How do I find x and y values?

I know the values ​​a, b and r. (x-a) ^ 2 + (y-b) ^ 2 = r^2 providing the formula I want to calculate the x and y points . Thank you in advance for your help.

Answer 1

[Torsten]

theta = linspace(0,2*pi,100);
x = a + r*cos(theta);
y = b + r*sin(theta);
plot(x,y)

[busra dogru]

I don't want to draw. I want to calculate the x and y values ​​from the formula. Thank you for your answer.

[Torsten]

Take a look at the two lines above the plot command. These are some x and y values from the formula. If you want more, increase the value of 100 in the first line.

[busra dogru]

ok I'll try it. thank you.

[busra dogru]

a = 2;

b = 2;

r = 2;

syms x y

eqns = (x - a)^2 + (y-b)^2 == r^2;

s = solve(eqns, x, y);

I've worked with it before. How do you think if I want to do it this way?

[Torsten]

You can solve one equation for one variable, i.e. you can write x as a funcion of y or vice versa. But you can't solve one equation for two variables.

If you write

s=solve(eqns,x)

you get x as a function of y,

if you write

s=solve(eqns,y)

you get y as a function of x.

[busra dogru]

Now I understand better, thank you very much..

[busra dogru]

Hello again. I can calculate x and y points with your code. I'm trying to check if these points are in the binary image. I get the following error when I run the following code;

[b, a] = find(newImage);
      A = [a, b];
     [m,n] = size(A);

     
     B = 1;
     t = 1;
        while(t<51)
             for p=1:m
              while(B==1)
                    theta = linspace(0,2*pi);
                    x = A(p,1) + round(t*cos(theta));
                    y = A(p,2) + round(t*sin(theta));
                    x = x';
                    y = y';
                    if x == 0 
                       x = 1;                    
                    end
                    if y == 0
                       y = 1;
                    end
                    B = A(x,y);
                    t = t+1;
             
                end
             end
       
        end
disp(x,y);

Subscript indices must either be real positive integers or logicals.

Error in Untitled18 (line 79)

B = A(x,y);

What can I do to solve this error? Thanks in advance ..

[Torsten]

x and y are vectors of doubles of the same size as "theta" - so the setting B = A(x,y) doesn't make sense.