Ellipse Construction

Manipulate[
 u1 = {3 Sin[t], 2 Cos[t]} - {Sqrt[5], 0};
 u2 = {3 Sin[t], 2 Cos[t]} + {Sqrt[5], 0};
 n1 = u1/Norm[u1];
 n2 = u2/Norm[u2];
 Show[ParametricPlot[{3 Sin[x], 2 Cos[x]}, {x, 0, t}, Axes -> None,
   PlotRange -> {{-3.1, 3.1}, {-2.1, 2.1}}],
  Graphics[Join[
    {PointSize[Large], Red, Point[{{Sqrt[5], 0}, {-Sqrt[5], 0}}],
     Line[{{-Sqrt[5], 0}, {3 Sin[t], 2 Cos[t]}}],
     Line[{{Sqrt[5], 0}, {3 Sin[t], 2 Cos[t]}}],
     Blue, Point[{3 Sin[t], 2 Cos[t]}], Red, PointSize[Medium]},
    {Point[Table[{Sqrt[5], 0} + n1  i, {i, 0, Norm[u1], 0.4}]]},
    {Point[Table[{-Sqrt[5], 0} + n2  i, {i, 0, Norm[u2], 0.4}]]}
    ]]
  ], {t, 10^-4, 2 Pi}]