If you want to make a perfect curve, use the shape tool. It has a circle already made and you can create the size you need as you drag. If you wish to "eliminate" half the circle, just select one of the points on the side you wish to eliminate by using the pen tool. Hold the command key down and drag over the point to select it if you are on a mac, the control key if you are on a pc. Then just hit the delete key, and voila, half a circle.