How to (efficiently) generate and catch some data-set that has similar correlation?

 How to (efficiently) generate and catch some data set that has similar correlation?
Correlation[x1 = RandomReal[10, 10], y1 = RandomReal[10, 10]]
ListPlot[Thread[{x1, y1}], Frame -> True]
Correlation[x2 = RandomReal[10, 30], y2 = RandomReal[10, 30]]
ListPlot[Thread[{x2, y2}], Frame -> True]

I have started with some basic lines, which will generate some random points.
Call the {x1,y1} dataset 1 and {x2,y2} the dataset 2.

I then want to Catch the two set when they have similar Correlation, for example, both are 0.43 to 2 decimal places, then plot them side by side.

Or -0.453 to 3 decimal places, then plot them side by side.

What’s the best way to do it?

Thanks.

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