PPT Slide
The azimuthal equidistant projection has the property that all distances from the center are rendered correctly, to scale. It is also possible to do this from two points, yielding the so-called two-point equidistant projection. The world map is then contained within an ellipse, the eccentricity of which depends on how far apart the two points are. The points are at the foci of the ellipse. Can you see why it must be an ellipse? When the two points coincide the map is circular; when they are antipodal the map is a straight line. Azimuths are no longer correct, although there is also a map projection with directions correct from two points.
C.F. Close, 1934, “A Doubly Equidistant Projection of the Sphere”, Geogr. J., 83(2):144-145.