# Relation between scale factor and standard meridians/parallels

Let's use transverse Mercator with a custom zone, with central meridian 30, the zone is 3 degrees wide at the equator, with a scale factor k=1, it means that the cylinder touching the spheroid along the central meridian.

However, with scale factor k=0.9996, the cylinder is secant of the spheroid at two meridians, one at right of Central Meridian and the other at left. How to find these meridians for a given scale factor k at equator?

• OP, I removed the reference to a conical projection (Lambert conformal?) because it makes the question too broad. Please feel free to undo my changes if you disagree. – mkennedy Dec 4 '18 at 20:25
• Related: gis.stackexchange.com/questions/122703/… Please check it out. – mkennedy Dec 4 '18 at 20:27
• Would a spherical approximation be sufficient for you? Also, secant lines in transverse mercator do not follow meridians, so just to clarify, are you looking for the meridian (longitude) of the secant line at the equator only? Or at any given parallel? – FSimardGIS Dec 4 '18 at 21:40
• @RalphTee -- Spheroid = Ellipsoid – Martin F Dec 5 '18 at 20:28
• @MartinF You are right! I misread the definition (i.e., 2 axes of equal length vs 3 axes). I had deleted my previous comment to avoid confusion. – Ralph Tee Dec 6 '18 at 2:03