TransformedRegion and RegionPlot

 TransformedRegion and RegionPlot

I encountered an issue using RegionPlot together with rotated regions. Notice how as long as one drags a slider in this simple Manipulate the plot behaves as one would expect, but reevaluates as soon as the slider is let go (and takes an suspiciously long time doing whatever it does). This question might, or might not be relevant (using DiscretizeRegion does not fix anything in this case however).

parabola[a_, b_] = ImplicitRegion[x - b y^2 > a, {x, y}]

TransformedRegion[parabola[a, b], 
RotationTransform[w, {a, 0}]], 
PlotRange -> {{0, 5}, {-3, 3}}], 
{a, 1, 2}, {b, 0, 2}, {w, -45°, 45° }]

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