I think you are trying to find out if you may get Ovarian Cancer because your grandmother had Ovarian. The answer is twofold because there are so many unanswered questions in this field:
1) Genetics: Yes, there is a connection ONLY with the BRCA1 and BRCA2 genes, but this is only 5 to 10 percent. And without any genetic testing of your grandmother and yourself for these genes, it's almost impossible to know. And even then, it's still a small percentage. Here is more info: http://www.mskcc.org/mskcc/html/8623.cfm
2) Similarities: Breast, Prostate, Ovarian cancers are all 'similar' in one aspect, but are not. That means if you have a family history of any of these cancers, then theoretically, yes, you could get ovarian. But that's just theoretically. You could still proceed with a normal life without ever contracting it.
So, if you are getting regular ultrasounds (etc) due to your cysts, that might be a plus that they can see any abnormalities. Any Ovarian Cancer caught in Stage 1 has a high survival rate...like 90 to 100% because it's never spread outside the ovaries. This may be more of a discussino between you and your gyn. but there might be a discussion about removing your reproductive systems if this is a serious conern to you.
One thing you can always do is monitor yourself (like all women should) for signs of ovca (yet they unfortunatley mimic other common and less serious conditions): http://www.mayoclinic.com/health/ovarian-cancer/DS00293/DSECTION=symptoms
I've had both cancers.
Oddly enough, I tested negative for the BRCA genes and another gene linking ovarian cancer and colon cancer. But, the docs thought my case was interesting, so I gave several vials of blood for research. Maybe there's a gene not yet discovered.
The link between mine seems to be the dependence on estrogen. I know that sounds obvious, but many female cancers are not dependent on it. Mine both were.
Good luck to you. It's always better to be cautious.
There are some links between the two, but I am not an expert on the subject. I am sure someone who knows more than me will be along.
Could you please not write in all caps. It makes it very hard to read and I am sure you don't know this, but writing in all caps is the internet equivalant of screaming at someone and I am sure you didn't mean it like that.
Oh, it is also helpful if you fill out some things in your profile so that we know a little bit more about you when we try to respond to your posts.
Jan