1. Since you are adult you need to furnish property details of your own only. The property belongs to your parents does not own by you and hence there is nor requirement to furnish such details.
2. If the column asking for property details is silent on the details of property of your parents which is most unlikely there is absolute no need to do so.
3. For your career do not think of abandoning your parents. They are more important than your career. Keep this in mind for ever.
All the best.