The Cartesian equation for the ellipse defines the curve by a simple parametric form with the x and y coordinates having different scalings:
x = a cos(t)
y = b sin(t)
where
a = primary radius
b = secondary radius
Note that t is a parameter that does not have a direct interpretation in terms of an angle. However, the relationship between the polar angle (theta) from the ellipse center and the parameter t follows from:
theta = arctan((b/a)*tan(t))
or
t = arctan((a/b)*tan(theta))
Therefore, to specify the red arc in the above diagram, in the counterclockwise direction, the following values would need to be set on the feature:
fme_geometry_type = fme_point
fme_type = fme_arc
fme_primary_axis = a = 2.0
fme_secondary_axis = b = 1.5
fme_rotation = thetaR = 10 (degrees)
fme_start_angle = tS = arctan((a/b)*tan(thetaS)) = arctan((2.0/1.5)*tan(45)) = 53.130102354155978703144387440907
fme_sweep_angle = tE - tS = arctan((a/b)*tan(thetaE)) - tS = arctan((2.0/1.5)*tan(180)) - tS = 180.0 - tS = 180.0 - 53.130102354155978703144387440907 = 126.86989764584402129685561255909
Coordinates should contain a single point, which is the center origin.