Question

Imaginary line going north and south parlays to the equator

Answer 1

One way of calling these lines is a "line of longitude" and another, and I think this is the word you were looking for, "meridian".
One example of this line is the prime Meridian, the line that goes through the Greenwich observatory and was chosen as the line dividing the two hemispheres.

Answer 2

The imaginary lines perpendicular to the equator on
the Earth's surface are the meridians of longitude.