Dy/dx=infinity ⇔ parallel to y axis , right?
i can't understand this logically.
by the way, i'm japanese, so if there's any mistakes in my english, let me know.

Your English is perfect.

Yes the statement is right.

Dy/dx = should me slope in this case.

A  slope of value zero is a horizontal line on the x and y coordinates.

A slope of value infinity is a vertical line on the x and y coordinates.

Since for an infinity, the line is vertical line on say a graph sheet.

So a vertical line drawn on any graph sheet would be parallel to your y axis on the graph sheet.

I hope this helps.

If it doesn't just let me know.