Question

用matlab求函数表达式

方程组为：sqrt((x4-x3)^2+(y4-y3)^2)=a； (x4-x3)*(x2-x1)+(y4-y3)*(y2-y1)=0
a为定值，求解x4 y4的表达式。
如果需要，还有以下条件，f已知：

y1=x1^2/(4*f);y2=x2^2/(4*f);x3=(x1+x2)/2;y3=(y1+y2)/2;

Answer 1

clear;clc
syms x1 x2 x4 y4 f a
y1=x1^2/(4*f);
y2=x2^2/(4*f);
x3=(x1+x2)/2;
y3=(y1+y2)/2;
eq1=sqrt((x4-x3)^2+(y4-y3)^2)-a;
eq2=(x4-x3)*(x2-x1)+(y4-y3)*(y2-y1);
D=solve(eq1,eq2,x4,y4);
x4=D.x4
y4=D.y4

追问

Warning: Explicit solution could not be found.
> In solve at 98
tangram_guid_1358859679360? Error using ==> subsref
No appropriate method, property, or field x4 for class sym.
Error in ==> sym.subsref at 17
y = builtin('subsref',x,a);

追答

>> syms x1 x2 x4 y4 f a
y1=x1^2/(4*f);
y2=x2^2/(4*f);
x3=(x1+x2)/2;
y3=(y1+y2)/2;
eq1=sqrt((x4-x3)^2+(y4-y3)^2)-a;
eq2=(x4-x3)*(x2-x1)+(y4-y3)*(y2-y1);
D=solve(eq1,eq2,x4,y4);
x4=D.x4
y4=D.y4

x4 =

1/32*(x1^3+x2*x1^2+16*f^2*x1-4*x1/(1024*f^2+128*x1*x2+64*x1^2+64*x2^2)*(32*x2*x1^3+32*x1^2*x2^2+16*x2^4+16*x1^4+256*f^2*x1^2+256*f^2*x2^2+32*x2^3*x1+512*(2*x1*x2*a^2*f^4+16*f^6*a^2+x1^2*a^2*f^4+x2^2*a^2*f^4)^(1/2))+x1*x2^2+16*f^2*x2-4*x2/(1024*f^2+128*x1*x2+64*x1^2+64*x2^2)*(32*x2*x1^3+32*x1^2*x2^2+16*x2^4+16*x1^4+256*f^2*x1^2+256*f^2*x2^2+32*x2^3*x1+512*(2*x1*x2*a^2*f^4+16*f^6*a^2+x1^2*a^2*f^4+x2^2*a^2*f^4)^(1/2))+x2^3)/f^2
1/32*(x1^3+x2*x1^2+16*f^2*x1-4*x1/(1024*f^2+128*x1*x2+64*x1^2+64*x2^2)*(32*x2*x1^3+32*x1^2*x2^2+16*x2^4+16*x1^4+256*f^2*x1^2+256*f^2*x2^2+32*x2^3*x1-512*(2*x1*x2*a^2*f^4+16*f^6*a^2+x1^2*a^2*f^4+x2^2*a^2*f^4)^(1/2))+x1*x2^2+16*f^2*x2-4*x2/(1024*f^2+128*x1*x2+64*x1^2+64*x2^2)*(32*x2*x1^3+32*x1^2*x2^2+16*x2^4+16*x1^4+256*f^2*x1^2+256*f^2*x2^2+32*x2^3*x1-512*(2*x1*x2*a^2*f^4+16*f^6*a^2+x1^2*a^2*f^4+x2^2*a^2*f^4)^(1/2))+x2^3)/f^2

y4 =

1/2/(1024*f^2+128*x1*x2+64*x1^2+64*x2^2)*(32*x2*x1^3+32*x1^2*x2^2+16*x2^4+16*x1^4+256*f^2*x1^2+256*f^2*x2^2+32*x2^3*x1+512*(2*x1*x2*a^2*f^4+16*f^6*a^2+x1^2*a^2*f^4+x2^2*a^2*f^4)^(1/2))/f
1/2/(1024*f^2+128*x1*x2+64*x1^2+64*x2^2)*(32*x2*x1^3+32*x1^2*x2^2+16*x2^4+16*x1^4+256*f^2*x1^2+256*f^2*x2^2+32*x2^3*x1-512*(2*x1*x2*a^2*f^4+16*f^6*a^2+x1^2*a^2*f^4+x2^2*a^2*f^4)^(1/2))/f

>>