Good! Now I can work

You can either use a diamond blade to cut the hole larger or a grinsing cup, unless the radius of the curve is very small, like 3" or less, in which case you should use a grinding drum. I prefer the grinding cup as it is quick and your chipping will be minimal (which really is not important as it is a drop in sink). The diamond blade when it is cutting through can always catch a vein producing a large crack, chip or other problem.
Try This:
http://www.defusco.com/5811-brazed-concave-cup-med-p-2007.htmlThis grinding cup will screw onto a grinder. It has a medium sized diamond grit so while it is still plenty aggressive it is not so aggressive as to rip out a vein. Realistically you could enlarge a 10" circle with this tool to a 12" circle in 20 minutes or less on 3/4" marble.
When finished, seal this with Hydrex to prevent the stone from getting etched by chemicals. This sealer is impregnating and will stain-proof your stone also.
http://www.defusco.com/tenax-impregnator-and-sealer-liter-p-1436.htmlMark