I am using Maxima to find an algebraic solution to an ellipse passing through three points.
The implicit form of an ellipse with center (uc,vc), angle a and ratio k between major and minor axis lengths is:
G := k^2*((u-uc)^2*sin(a)^2-(u-uc)*(v-vc)*sin(2*a)+(v-vc)^2*cos(a)^2)+(u-uc)^2*cos(a)^2+(v-vc)^2*sin(a)^2+(u-uc)*(v-vc)*sin(2*a)-D=0
Assume three points with coordinates (u1,v1) (u2,v2) (u3,v3) which the ellipse passes through with k and a given. I then need to determine uc,vc and D
So, I generate three equations substituting u for u1 and v for v1 and so on.
After that I use linsolve to get the solution for uc,vc and D.
The equations get very long.
My problem is that these equations does not seem to give the right answer numerically. I try three points and using the derived values for uc,vc and D does not solve G to be equal to 0.
Could this be a bug in Maxima or am I missing something fundamental?
Thanks
/Jonas Forssell, Gothenburg, Sweden
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