In UWP there is a different component to do this job. It's called the Composition API and is available in the NuGet Package "Win2D.uwp".
Basically you'll need to get the compositor for your visual object with
_compositor = ElementCompositionPreview.GetElementVisual(this).Compositor;
and create a drop shadow using the compositor.
_compositor = ElementCompositionPreview.GetElementVisual(this).Compositor;
// create a red sprite visual
var myVisual = _compositor.CreateSpriteVisual();
myVisual.Brush = _compositor.CreateColorBrush(Colors.Red);
myVisual.Size = new System.Numerics.Vector2(100, 100);
// create a blue drop shadow
var shadow = _compositor.CreateDropShadow();
shadow.Offset = new System.Numerics.Vector3(30, 30, 0);
shadow.Color = Colors.Blue;
myVisual.Shadow = shadow;
// render on page
ElementCompositionPreview.SetElementChildVisual(this, myVisual);
The downside beeing, that this is not quite straight forward. You can use different brushes to display images, solid colors or other stuff, it won't apply to existing visuals on screen (as far as I understand it). You can read more about the basics here. Probalby you'll need to use a surface brush, which can hold a wide variety of different visual types, like images. Currently it does not look like there is a ready made component for ellipses though.
Alternatively there exists a xaml extension which will do all that stuff for you using pure xaml, might be worth a shot and maybe also support ellipses.
As an ending note, all of this is currently a work in progress on microsofts part and should become a native part of the UWP API in the future.