Draw Longitude Lines of a Sphere on a Circle

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Bking592
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Homework Statement
Find formula for putting curve to put longitude lines of the 2D circle
Relevant Equations
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I'm trying to draw a 2D globe
 

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Welcome to PF.

What can you tell us about Mercator's projection? Are there any other projections that you could consider using?
 
The lines of longitude will look like half-ellipses on the face of the 2D globe.
You need to find out how to draw an ellipse.