The follosing system of equation have 6 solution (ct=8,8,8,8,7,9) but mathematica don't give any why?:

    NSolve[{Sqrt[EAx^2 + 0.0625 EAy^2] (EBx) + (EAx) Sqrt[
     EBx^2 + 0.0625 EBy^2] == 0, 
  0.25 Sqrt[EAx^2 + 0.0625 EAy^2] EBy + 
    0.25 EAy Sqrt[EBx^2 + 0.0625 EBy^2] == 0, 
  EAy - EBy == 0, -1 + 4 EAx^2 + EAy^2 == 0, -1 + 4 EBx^2 + EBy^2 == 
   0, -8 + ct + EAx - EBx == 0}, {ct, EAx, EAy, EBx, EBy}, Reals, 
 WorkingPrecision -> 13]

The following system of equations has $6$ solutions $(ct=8,8,8,8,7,9)$ but Mathematica doesn't give any solution:

NSolve[{ Sqrt[EAx^2 + 0.0625 EAy^2] (EBx) + (EAx) Sqrt[
              EBx^2 + 0.0625 EBy^2] == 0, 
         0.25 Sqrt[EAx^2 + 0.0625 EAy^2] EBy + 0.25 EAy Sqrt[EBx^2 + 0.0625 EBy^2] == 0, 
         EAy - EBy == 0, 
         -1 + 4 EAx^2 + EAy^2 == 0, 
         -1 + 4 EBx^2 + EBy^2 == 0,
         -8 + ct + EAx - EBx == 0},
       {ct, EAx, EAy, EBx, EBy}, Reals, WorkingPrecision -> 13]

 NSolve::infsolns: Infinite solution set has dimension at least 1.

 Returning intersection of solutions with 
  (38650 ct)/65167-(41688 EAx)/65167-(153968 EAy)/195501+(185938 
   EBx)/195501+(153196 EBy)/195501 == 1. >>

 {}

Why ?