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The goal is to create an image like the one below

Desired output

which was created using

ParametricPlot[{t, t^2}, {t, 0, 1}, Epilog -> Disk[{0.5, 0.5}, 0.09]]

but instead of using the Graphics primitive I want to use a Rasterized version of Disk.

Using the commands below, how can I duplicate the result?

bkgd = Rasterize[Disk[{0, 0}, 0.09]];
pplot = ParametricPlot[{t, t^2}, {t, 0, 1}];

It is important that ParametricPlot remain un-Rasterized.

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First, you have to define bkgd differently because it's not a disk unless you make it a Graphics first:

bkgd = Rasterize[Graphics@Disk[{0, 0}, 0.09]];

Then use Inset:

ParametricPlot[{t, t^2}, {t, 0, 1}, 
Epilog -> {Inset[bkgd, {.5, .5}, Automatic, .2]}]

Disk in plot

The position and size of the disk image are controlled by the last three arguments of Inset.

You will note that the last argument (the size scale) is a factor relative to the plot region (with 1 corresponding to the whole width).

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