The questioner intended to investigate, but he was not sure at F 1 and F2, which indicated that the left focus might be F 1 or F2, and the result was wrong.
The counterevidence is as follows: For this hyperbola, the focal length 2c= 12 is fixed; Let's set the left focus F 1 and the right focus F2. If there is a point p on the hyperbola, the distance to F 1 is 1, and the distance to F2 is 9. According to the sum of two sides of a triangle, it is greater than the third side, 9+ 1= 10, but less than 12, so it is impossible to have this point.
In fact, you can find the minimum distance from the left branch of hyperbola to the left focus. How did you find it yourself?