I purchased a domain name and hosting account,which is active,and now i want to purchase another domain name and link it to the previous hosting account instead of paying for another hosting account for the new domain name.
Pls,how do i go about it?

There is what is call addon in hosting account, just point your name server to already hosting account nameserver and use addon to add the domain, with this you will be using one hosting account in multiple domain. But your hosting provider must support this feature.
I don't if your our Customer we have help you do this as we support the feature.

Thank you for your response
.

Mr perfect has said it all, I believe you'll able to point your domain to your hosting name servers from your domain cp. The only problem you can encounter is, if your hosting plan do not support addon domain like mrperfect said.

Does this mean I will be pointing the new domain name to the existing one or the new domain will exist independently of the existing one....i.e. I will be able to set up an new website independently of the existing one.

BOLAJIAJANI: Mr perfect has said it all, I believe you'll able to point your domain to your hosting name servers from your domain cp. The only problem you can encounter is, if your hosting plan do not support addon domain like mrperfect said.

can you give me a step by step guide?

Go to your domain control panel, look for where you can change your name servers, probably by clicking the domain name.
Change the name servers to your webhosts' e.g in d format ns1.host.com and ns2.host.com or let me just say nsnumber.host.com at least put two name servers.
After that is done go to your host cp, then click on addon domain. You'll be asked to fill in your domain name, ftp, document root, password, e.t.c. that's all.
To your question, yes it is independent on original domain.