How Do I Erase Hard Drive Without OSX Disk?

You don't, you have to call AppleCare and order a replacement set of original DVDs. The cost is nominal however you will need a credit card and the computer's serial number. This will be a valuable service too for whoever gets your iMac.

You can also order a OS X Snow Leopard disc directly from Apple, you can buy that from the online store. Once you have either DVD boot from it, launch Disk Utility and do a erase and install.

Without one of those dvds you cannot do and erase.

Macs can boot Linux. If you are willing & able to burn a CD (or create a USB bootable disk) you can erase the Mac via Linux.

Ubuntu live CD's have a tool (also called Disk Utility) that can reformat disks & erase data on connected disks.

Or you could use DBAN…

http://www.dban.org/

or any 'universal boot disk' that has disk erase tools installed.

http://www.ultimatebootcd.com/

Just avoid having any disks connected that you do not want to be wiped, it is very easy to erase the wrong thing.

Post more info about your Mac if you want to try using Linux - e.g…

Do you have a CD drive?

Do you have another machine to make a CD or USB bootable system?

How much experience do you have with other OS's?

Another option is to use Target Disk mode & erase the iMac's HD from another Mac or PC if you have leads to connect it via Firewire or Thunderbolt…

How to use and troubleshoot FireWire target disk mode - Apple Support

You don't need the original disks to erase a disk - it just makes the process easier.

You can also download 10.10 from the store & install OS X to a USB disk & then use that to erase the internal disk. You state the iMac supports 10.9, so it will also run 10.10 which is free on the App store.

You can reinstall from any running OS X that has the App store (by re-downloading it) or you can write the installer to a USB drive so you can reuse it.

Create a bootable installer for OS X Mavericks or Yosemite - Apple Support

What you have to consider is that it is against the Apple EULA to sell a Mac with an OS that you personally own - OS X from the App store is only licenced to you. Ideally you pass on any Mac with the original OS & disks or without Mac OS (Linux is free & can be passed on).

It is not clear to me what the state of this Mac is in, If yo have a recovery partition you can boot into recovery mode & then you can erase the volume that the OS is installed on via Disk Utility.

A new owner would boot into recovery mode & enter their own Apple ID to install an OS that is in their App store purchases.