Hello,
I wanted to see if Mathematica 9.0.1 (64bit under Linux) can solve a simple problem from Analytical Geometry: to derive the ellipse's equation from the fact that the sum of distances to the foci is a constant with the given coordinates of the foci: F1(Sqrt[a^2-b^2],0) and F2(-Sqrt[a^2-b^2],0).
PF1 = Sqrt[(x - Sqrt[a^2 - b^2])^2 + y^2];PF2 = Sqrt[(x + Sqrt[a^2 - b^2])^2 + y^2];sol = Solve[PF1 + PF2 == 2*a, y]
This produced the correct solutions. However, when I wanted to let Mathematica verify them it failed, i.e.
(PF1+PF2) /. sol // FullSimplify
did NOT produce {2*a, 2*a}. Please see the attached nb file. So, my question is: is there some way of forcing Mathematica to verify this solution correctly?
I tried the same thing on Maple 17 (64bit Linux) and it behaved exactly the same as Mathematica, i.e. solved the equation correctly but could not verify the solution by substituting it into the expression PF1+PF2 or other expressions like (PF1+PF2)^2 - 4*a^2. On Reduce it could not even solve it, let alone verify...
Any ideas?
Kind regards
Tigran
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