|First of all, your slimline case requires that any add in cards be of the low profile type. The card you ask about doesn't appear to be low profile. That card requires a 450W minimum power supply and needs a 6 pin PCIe power connector. |
The specs from HP for your computer don't state anything about your power supply. Open the case and see if you have a 6 pin PCIe power connector. The link below shows what that connector looks like. Any powerful card will require at least one 6 pin connector. Some require more. That means a better power supply than you may currently have.
Shop for low profile cards. Some are shipped with both low profile and standard brackets.
The 450W spec is just a guide. You need a name brand power supply. That card draws 108W at full power which pulls 9A from the +12V rail.
Post back before buying anything.