圆形对象根据Matplotlib中的图像保存格式更改位置

I have to place a circle in a specific spot in an image. The problem is that the image is plotted in an semi-log scale, which distorts the circle unless I use some specific transform. However, when I do that, the circle changes position depending if I save the image as A PDF or PNG. Here's a MWE:I have to place a circle in a specific spot in