Was F1 2010 Released on PlayStation 2? No

No. F1 2010 (Codemasters) was released September 2010 on:

• PlayStation 3
• Xbox 360
• Microsoft Windows (Games for Windows Live / Steam)

The PlayStation 2 was discontinued in Japan (Dec 2012) / Worldwide (Jan 2013), but major publishers had largely abandoned it by 2010. The last major multi‑platform racing title on PS2 was likely Need for Speed: Undercover (2008) or FIFA 14 (Legacy Edition, 2013 – roster update only). F1 2010 required the EGO Engine 1.0 (DX11/Shader Model 4.0) which the PS2 (GS+VPU) could not support.

If you want F1 on PS2, your options are Formula One 2001 – Formula One 06 (Studio Liverpool / Sony) or F1 Career Challenge (EA, 2003).