Something like this?
curves = ParametricPlot[{{4 Cos[t], 5 Sin[t]}, {Cos[2 t]/(t + 3), 3 Sin[t]}}, {t, 0, 2 Pi}]; Animate[Show[curves, Graphics[{PointSize[Large], Point[{4 Cos[t], 5 Sin[t]}], Point[{Cos[2 t]/(t + 3), 3 Sin[t]}]}]], {t, 0, 2 Pi}]
This was exactly what I was looking for! Thank you so much.
I don't Know if that what you want exactly but maybe help you