Fortunately, if this picture I have of the motherboard is correct, the PCIe slot is not at the end, thus, you could use a low-profile card with a taller-than-single-slot cooler.
Even more of a curse is something like my old Dell Inspiron 3647 Small Desktop. It required low-profile, AND the PCIe slot was all the way at the end of the case, so it had to be single slot with a short cooler for the GPU, otherwise it would've butted up against the side of the case. It was a weird sort of design that looked like a reverse, upside-down install of the MB, with the PCIe slot located right at the edge, thus positioning the video card such that the cooler was facing away from the rest of the motherboard.
Is it a 1050Ti that requires a 6-pin power connector, or no? Hopefully one of those that does NOT need it. The power supplies on the small form-factor systems usually don't include those.
Do you know what the power supply is rated at? Also, if you can get a look at the side label that shows how many amps are on the 3.3V, 5V, and 12V rails, it will reasonably indicate whether there's enough power available for that card.
The 1050Ti doesn't require a huge amount of power, but some of those power supplies on the small systems are really limited. My Dell, for example, was rated at 220W total, with 18A (thus 216W) available on the 12V rail.
There's a label on the bottom in that pic I showed - if you can read that label, it'll say things about the various 12V, 5V, and 3.3V stuff. May not be accessible.
I saw one online that claims to be for the Elite 8300SFF (https://www.ebay.co.uk/p/HP-Elite-8300-SFF-Power-Supply-240w-613762-001-UK-SELLER-Drop/5011040196) that said 16A for 12V main, and 16A for 12Vcpu. See the zoomed-in view of the 4th picture.
If that's correct, and if your 8200 uses the same power supply as the 8300, then you should be good to go. It may even have the 6-pin connector if your card needs it -but I'm not 100% sure that what I'm looking at is the correct one.
just a quick one what about the GTX 1050 ti mini would that work as well...and last thing are there other makes of the GTX 1050 ti other then MSI that don't need 6 pin power connectors to run them. Thanks .