Parametric plot and points [closed]

How I can add points to curve that has been plotted as parametric plot?

I am working on the brachistochrone example and I want to plot part of the cycloid, direct line and some combinations of them into same image.

How I can do this?

closed as off-topic by Bob Hanlon, MarcoB, bbgodfrey, Young, EdmundAug 22 '16 at 9:55

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Bob Hanlon, MarcoB, bbgodfrey, Young, Edmund
If this question can be reworded to fit the rules in the help center, please edit the question.

• Have you seen the options Epilog and Prolog? You can also use Show[] to combine your plot with other Graphics[]. – Michael E2 Aug 21 '16 at 19:40
• Sorry no I haven't. I am very new with Mathematica. I will look into these. – Zzz Aug 21 '16 at 19:45