How do i Know

As long as it has a PCI-E x16 slot it will support any modern graphics card. Computers are basted on standards. Your biggest worry will be whether your power supply meets the requirements of the graphics card and it if will physically fit in your case.

Where do i check the power supply..
i have DELL slim CPU..
Yes it has PCI-E x16 slot.
I bought 8400gs it didnot fit so i removed the steel bar with Bought outlets
now it fits. The Monitor Outlet is hanging, But it is working.
Fitting the graphic is not a problem.
Plz just tell me how do i find the power supply
and what to look for with Graphic card.

If it is a slim design I do not believe it will fit a standard card. You need a low profile card. The lower end cards are usually your only choice.

The power supply specs are printed on the side of the unit inside your case.

Can you tell me low profile card better then 8400gs which i should buy.

We need to know your power supply specs first. wattage and 12V wattage and Amp rating.

I am guessing you will end up with a 5570 or something of that nature.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

SAPPHIRE 100293DP Radeon HD 5570 1GB 128-bit DDR3 PCI Express 2.1 x16 HDCP

This card is ddr3
my 8400gs is ddr2
Will it work in my cpu

You need to verify your PSU is adequate. The 5570 has a max board power usage of 39Watts. I am sure this is more than the 8400GS. Even though that is not alot, you will want at the bare minimum 300W on your power supply.

I just checked the power supply says max output is 210w..
will it work.
is DDR2 and DDR3 an issue.
Thank You

I wouldn't try it. Those are really intended for onboard video only. The 8400gs is a very lower powered card so that is why it was fine.

is is possible to upgrade PSU of
DELL GX280

The slimline PC's usually can not be upgrade. You MIGHT be able to find a replacement PSU that has a few more watts, but that is about all. I doubt it. Those small form factors are not meant to be upgraded all that much.