How can I exclude a point from a Region Plot?

Questions
1

I want to exclude the point {0,0} from: RegionPlot[0 < x^2 + (y^2)/4 <= 1 , {x, 2, -2}, {y, 2, -2}]

2

I can exclude a small region around {0,0}

RegionPlot[
 0 < x^2 + (y^2)/4 <= 1 && x^2 + y^2 > .03, {x, -2, 2}, {y, -2, 2}]