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Hey Frances! Good question here. Most likely, the best solution is  to host the content on a subdirectory of the same root domain ( www.mysite.com/mylove). You're right that if you create a new domains, you will need to build links/authority/trust to a completely new domain. This may make it more difficult for the page to compete in the SERPs. Keeping the same root domain will allow you to leverage any authority you've built.