Don't do the clear!
Instead of drawing on your form, create a simple Panel class:
public class MyPanel : Panel
protected override void OnPaintBackground(PaintEventArgs e)
The only purpose of this is to disable background clearing.
Add the MyPanel to your form.
Now draw your ellipse on the panel, in the Paint event.
What I would do is to create a region which is the elipse:
GraphicsPath path = new GraphicsPath();
Rectangle rect = new Rectangle(0, 0, 100, 100);
Region myClearBit = new Region();
This will draw a red circle on a green background, and shouldn't flicker as it re-sizes.