Use the Elliptical Marquee tool at the top left of the Toolbox to make a selection.
1. To keep the ellipse circular hold down the Shift key as you drag.
2. If you hold down the Alt key before you drag the ellipse will be drawn from the centre out rather than from one corner.
Now, you have a selection which if you press the backspace key will be deleted and replaced with the current background colour. So first click on the background colour well and choose the colour you want, in this case I choose a deep blue.
Since we don't actually want to delete the centre of the ellipse, but rather delete everything else, choose Select>Inverse or use the shortcut keys Ctrl-Shift-I or Cmd-Shift-I .
To get a soft edge set a feather value before you delete - Select > Feather... and enter a value between 0.2 and 250. The value you choose will create a faded area that size on either side of the dotted selection line.
To judge the amount to get your desired effect it helps to know the resolution of your image. Web images are usually just 72 dpi so a value of 36 would be half an inch (just over a cm) while the print industry routinely scans at 300dpi so with that high resolution 36 would be only about a tenth of an inch or just over 0.25 cm. If the results are different from what you were hoping for just step backwards twice (the first undoes the deletion, the second resets the feather value) (shortcuts Ctrl-Alt-Z or Cmd-Alt-Z) and try a new value.