Understanding parked domains

Trying to see the best way to handle this from google POV

[Clark]

I thought it was ok to park domain2.com on top of domain1.com. When I use my ISP's park a domain, the way it will work is, if the main domain is domain1.com and the full url is:

[domain1.com...]

if I try the parked domain, it will look like

[domain2.com...]

only it will point to the same page.

Is this the wrong way to handle it in google? Is it better to do something else?