Is Solve[] very inefficient in solving equations involving square roots?
The input below attempts to find out the explicit expression of either x or y in terms of other variables {x|y, a, c}, and c is the focal length, a is directrix.
F = (Sqrt[(x+c)^2+y^2]-Sqrt[(x-c)^2+y^2]==2a && x>0 && c>0 && a>0 && c>a)
Solve[F,y]
Solve[F,x]
After running on my Acer dual core laptop for over 4 hours this input is still shown in “running” state.
http://reference.wolfram.com/mathematica/ref/Solve.html
“Solve deals primarily with linear and polynomial equations.”
So is the equation above an example that Solve[] works not so well with equations involving square roots (and likely other order roots) ?