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how can I solve two equations with two unknown variable using matlab?

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I want to solve two equations with two unknown variables I have two equations (-x)*(x1 - x) + (r - y)*(y1 - y) = 0, (x1 - x)^2 + (y1 - y)^2 = z^2, where, x1,y1,r and z are known values. The values can be used as the inputs to the program.
what I tried is,
syms x y
eqns = [x^2 +y^2 - x*point_x - y*point_y + r*point_y - r*y == 0 ,...
(point_x - x)^2 + (point_y - y)^2 == length_tang^2];
vars = [x y];
[a,b] = solve(eqns,vars);
but it takes too much time and then gives no values.
  2 comentarios
John D'Errico
John D'Errico el 17 de Abr. de 2018
Editada: John D'Errico el 17 de Abr. de 2018
You say that x and y are unknowns. x1, y1, z are knowns.
(-x)*(x1 - x) + (r - y)*(y1 - y) = 0,
Then what is r? It is not an unknown. It is not known. Something in the middle perhaps? I also see an r1. Is it related to r? Is it known? Unknown? Quasi-known?
Avi
Avi el 17 de Abr. de 2018
sorry for that. I have edited the question. there is only one r and it is known.

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Respuesta aceptada

John D'Errico
John D'Errico el 17 de Abr. de 2018
Editada: John D'Errico el 17 de Abr. de 2018
point_x = 2;
point_y = 4;
length_tang = 1
r = 5;
syms x y
E = [(-x)*(point_x - x) + (r - y)*(point_y - y) == 0, (point_x - x)^2 + (point_y - y)^2 == length_tang^2];
S = solve(E,x,y)
S = 
  struct with fields:
      x: [2×1 sym]
      y: [2×1 sym]
S.x
ans =
   2
 6/5
S.y
ans =
    5
 17/5

Too slow? It came back virtually instantaneously.

timeit(@() solve(E,x,y))
ans =
      0.19394

0.2 seconds is too slow?

Note that it is probably possible for SOME sets of inputs, there is no real valued solution at all.

  2 comentarios
Avi
Avi el 17 de Abr. de 2018
Thank you your answer works, but is slow as I have to solve it 51*61. Is there any way to increase the speed of the solution?
Torsten
Torsten el 18 de Abr. de 2018
Yes, you can get the general solution for point_x, point_y and r defined as "syms" and then substitute the 51*61 values for which you want to evaluate this solution.
help subs
Best wishes
Torsten.

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Torsten
Torsten el 17 de Abr. de 2018

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