I reverse engineered GPT-image-2’s ratio system, if you are struggling to control the output ratio, use this chart

So it turns out GPT-image-2 is using a special type of ratio control, and you need to specify it in the prompt, there is no dedicated control in the API.

To do so with the API, only the ratio itself won't work 90% of the time. You need to append a phrase like this in your prompt:
Output in exactly 1774px x 887px (2:1 ratio) resolution landscape format.

Say that you want to create a 5:4 ratio image, you need to find that 5:4 means the resolution is basically 1402x1122, and you can use this combination in the above appended phrase.

In my 100+ tests, this phrase works 100% of the time. with only the resolution or ratio, the success rate drops significantly.