The relation between a confusion matrix and a ROC curve

As an example I have a confusion matrix that shows good accuracy but poor performance on sensitivity because of imbalanced classes. I made this fictive table for a presentation.

                actual          actual
positive        negative
pred. positive      6              20
pred. negative      6              986


I have two questions:

First, is it possible to draw a ROC curve that matches with this confusion matrix and how to do this without having the original data? Is there an easy/short way or should I somehow reconstruct some "fictive" data.

Second, could different ROC curves potentially match with the same confusion matrix? I thought that classification thresholds may differ and therefore may result in different ROC curves with similar confusion matrix (see Fawcett 2006.

For implementation I am using the ROCR package in R.

This matrix is just a point on your ROC curve obtained for the threshold you picked. You can compute a value of sensitivity and specificity with your matrix, this is where you point is. $$sensitivity=6/12=1/2$$ $$1-specificity=986/1006=0.98$$ Many different ROC curves could then cross this point. If you can move this threshold, you can draw your ROC curve.