The effect above is a simple and quick one to create using Illustrator.
All you need is an ellipse, a gradient and the Transform Effect tool. I don’t have the latest version of Illustrator but know the Transform Effect tool is available in CS6 and earlier. Hopefully, whatever version you’re using, you’ll be able to follow the tutorial and have fun with it.
You can download the free tutorial here:
Three Bees in My Bonnet 