If I understand correctly, you're referring to the non-EEA parent of an EEA national. The parent has been here less than 6 months.
If the parent is dependent on the EEA national and the EEA national is a qualified person, they can use form EEA (FM) to request a Residence Card:
https://www.gov.uk/government/publicati ... orm-eea-fm
However, if Brexit goes ahead, Residence Cards will become obsolete within the next couple of years - so the parent would be better off applying directly for Pre-Settled Status from 30 March via the link:
https://www.gov.uk/settled-status-eu-ci ... 2774a8dfb8
There is currently a test phase open for application, but in my opinion it's better to wait 3 weeks until the scheme officially opens on 30 March.