Cleaning LiDAR points that classification algorithm misses?

First of all, I would not call it the "imaginary axis" - the name needs to be clearer as to what the value on that axis represents. If I understand your question correctly, it is the imaginary $y$-axis; in other words, you're allowing $y$ to be a complex number $y=y_0+iy_1$, while you are still requiring $x$ to be real.

If I understand your question correctly, you are wondering if your plot of the solutions to $$\frac{x^2}{a^2}-\frac{(y_0+iy_1)^2}{b^2}=1$$ is correct. Well, I'd advise thinking about it like this: $$\frac{x^2}{a^2}-\frac{(y_0+iy_1)^2}{b^2}=\bigg(\frac{x^2}{a^2}-\frac{y_0^2}{b^2}+\frac{y_1^2}{b^2}\bigg)-i\bigg(\frac{2y_0y_1}{b^2}\bigg)=1$$ The only way this is possible is if $y_0=0$ or $y_1=0$; otherwise, the imaginary part of the left side is non-zero, while the imaginary part of the right size is zero.

Thus, you're looking for the solutions to $$\frac{x^2}{a^2}-\frac{y_0^2}{b^2}+\frac{y_1^2}{b^2}=1$$ where either $y_0=0$ or $y_1=0$. The above equation defines a hyperboloid of one sheet, and so you're looking for the intersection of that hyperboloid with the $xy_1$-plane (where $y_0=0$) and $xy_0$-plane (where $y_1=0$).

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In conclusion: Your plot seems to be of the right form, though it is not centered correctly (the center of the whole thing should be at the origin).

Most filesystems don't support inserting data at the beginning of a file, and Unix doesn't have an API for that. In most operating systems, the only ways to modify a file are to overwrite a segment (e.g. change aaaaaaaaaa to aaabbbaaaa), to append data at the end (e.g. change aaaaaaaaaa to aaaaaaaaaacccc), or to truncate the file (e.g. change aaaaaaaaaa to aaaaa).

If you want to add data at the beginning of a file, create a new file with the additional data, and copy the content of the old file after that.

This is true both for the original Unix and for most if not all modern ones (and more generally for most operating systems).