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已知x1,y1;x2,y2;R,y2的方程组(x1-x3)/(y1-y3)=(x1-x2)/(y1-y2);(x3-x2)*(x3-x2)+(y3-y2)*(y3-y2)=R*R;

题目详情
已知x1,y1; x2,y2; R ,y2的方程组
(x1-x3)/(y1-y3)=(x1-x2)/(y1-y2);
(x3-x2)*(x3-x2)+(y3-y2)*(y3-y2)=R*R;
▼优质解答
答案和解析
[x3,y3]=solve('(x1-x3)/(y1-y3)=(x1-x2)/(y1-y2)','(x3-x2)*(x3-x2)+(y3-y2)*(y3-y2)=R*R','x3','y3')
结果:
x3 =
-(x1*y2-1/2*x1/(-2*x1*x2-2*y1*y2+x1^2+x2^2+y1^2+y2^2)*(2*y2^3-4*x1*y2*x2-4*y2^2*y1+2*y2*y1^2+2*x1^2*y2+2*x2^2*y2+2*(4*x1*x2*R^2*y1*y2+6*y1^2*y2^2*R^2-4*y1^3*y2*R^2-4*y1*y2^3*R^2+x1^2*R^2*y1^2+x1^2*R^2*y2^2+x2^2*R^2*y1^2+x2^2*R^2*y2^2-2*x1*x2*R^2*y1^2-2*x1*x2*R^2*y2^2-2*x1^2*R^2*y1*y2-2*x2^2*R^2*y1*y2+y1^4*R^2+y2^4*R^2)^(1/2))-x2*y1+1/2*x2/(-2*x1*x2-2*y1*y2+x1^2+x2^2+y1^2+y2^2)*(2*y2^3-4*x1*y2*x2-4*y2^2*y1+2*y2*y1^2+2*x1^2*y2+2*x2^2*y2+2*(4*x1*x2*R^2*y1*y2+6*y1^2*y2^2*R^2-4*y1^3*y2*R^2-4*y1*y2^3*R^2+x1^2*R^2*y1^2+x1^2*R^2*y2^2+x2^2*R^2*y1^2+x2^2*R^2*y2^2-2*x1*x2*R^2*y1^2-2*x1*x2*R^2*y2^2-2*x1^2*R^2*y1*y2-2*x2^2*R^2*y1*y2+y1^4*R^2+y2^4*R^2)^(1/2)))/(y1-y2)
-(x1*y2-1/2*x1/(-2*x1*x2-2*y1*y2+x1^2+x2^2+y1^2+y2^2)*(2*y2^3-4*x1*y2*x2-4*y2^2*y1+2*y2*y1^2+2*x1^2*y2+2*x2^2*y2-2*(4*x1*x2*R^2*y1*y2+6*y1^2*y2^2*R^2-4*y1^3*y2*R^2-4*y1*y2^3*R^2+x1^2*R^2*y1^2+x1^2*R^2*y2^2+x2^2*R^2*y1^2+x2^2*R^2*y2^2-2*x1*x2*R^2*y1^2-2*x1*x2*R^2*y2^2-2*x1^2*R^2*y1*y2-2*x2^2*R^2*y1*y2+y1^4*R^2+y2^4*R^2)^(1/2))-x2*y1+1/2*x2/(-2*x1*x2-2*y1*y2+x1^2+x2^2+y1^2+y2^2)*(2*y2^3-4*x1*y2*x2-4*y2^2*y1+2*y2*y1^2+2*x1^2*y2+2*x2^2*y2-2*(4*x1*x2*R^2*y1*y2+6*y1^2*y2^2*R^2-4*y1^3*y2*R^2-4*y1*y2^3*R^2+x1^2*R^2*y1^2+x1^2*R^2*y2^2+x2^2*R^2*y1^2+x2^2*R^2*y2^2-2*x1*x2*R^2*y1^2-2*x1*x2*R^2*y2^2-2*x1^2*R^2*y1*y2-2*x2^2*R^2*y1*y2+y1^4*R^2+y2^4*R^2)^(1/2)))/(y1-y2)
y3 =
1/2/(-2*x1*x2-2*y1*y2+x1^2+x2^2+y1^2+y2^2)*(2*y2^3-4*x1*y2*x2-4*y2^2*y1+2*y2*y1^2+2*x1^2*y2+2*x2^2*y2+2*(4*x1*x2*R^2*y1*y2+6*y1^2*y2^2*R^2-4*y1^3*y2*R^2-4*y1*y2^3*R^2+x1^2*R^2*y1^2+x1^2*R^2*y2^2+x2^2*R^2*y1^2+x2^2*R^2*y2^2-2*x1*x2*R^2*y1^2-2*x1*x2*R^2*y2^2-2*x1^2*R^2*y1*y2-2*x2^2*R^2*y1*y2+y1^4*R^2+y2^4*R^2)^(1/2))
1/2/(-2*x1*x2-2*y1*y2+x1^2+x2^2+y1^2+y2^2)*(2*y2^3-4*x1*y2*x2-4*y2^2*y1+2*y2*y1^2+2*x1^2*y2+2*x2^2*y2-2*(4*x1*x2*R^2*y1*y2+6*y1^2*y2^2*R^2-4*y1^3*y2*R^2-4*y1*y2^3*R^2+x1^2*R^2*y1^2+x1^2*R^2*y2^2+x2^2*R^2*y1^2+x2^2*R^2*y2^2-2*x1*x2*R^2*y1^2-2*x1*x2*R^2*y2^2-2*x1^2*R^2*y1*y2-2*x2^2*R^2*y1*y2+y1^4*R^2+y2^4*R^2)^(1/2))