How to draw the shape in the comments?

[Arvind]

How to draw this shape in Ai?

[Monika Gause]

Use the ellipse tool and the line segments tool. Tehn use live paint or the shapebuilder tool 

[Arvind]

How to trim the unwanted curve or line?

[Monika Gause]

As I said: use the live paint respectively shapebuilder tool https://helpx.adobe.com/illustrator/using/creating-shapes-shape-builder-tool.html

[Jacob Bugge]

Arvind,

Or Pathfinder>Divide and Ctrl/Cmd+Shift+G to Ungroup.

And to answer your second questions, ClickDrag over the unwanted bits and Delete.