Add a new quarter curve object.

add_quarter_curve.py

import bpy
import math
from mathutils import Vector

class OBJECT_OT_quarter_circle(bpy.types.Operator):
    """Create one fourth of a circle."""
    bl_idname = 'curve.quarter_circle_add'
    bl_label = 'Quarter Circle'
    bl_options = {'REGISTER', 'UNDO'}

    def execute(self, context):
        curve_name = 'Quarter'
        curve = bpy.data.curves.new(curve_name, 'CURVE')
        spline = curve.splines.new('BEZIER')
        spline.bezier_points.add(count=1)

        # http://www.charlespetzold.com/blog/2012/12/Bezier-Circles-and-Bezier-Ellipses.html
        handle = 4 * math.tan(math.radians(22.5)) / 3

        pt0 = spline.bezier_points[0]
        pt0.co = Vector((1.0, 0.0, 0.0))
        pt0.handle_right = pt0.co + Vector((0.0, handle, 0.0))
        pt0.handle_left = pt0.co
        
        pt1 = spline.bezier_points[1]
        pt1.co = Vector((0.0, 1.0, 0.0))
        pt1.handle_left = pt1.co + Vector((handle, 0.0, 0.0))
        pt1.handle_right = pt1.co

        obj = bpy.data.objects.new(curve_name, curve)
        context.scene.objects.link(obj)

        return {'FINISHED'}

def custom_object_add(self, context):
    layout = self.layout
    
    layout.operator("curve.quarter_circle_add", icon='CURVE_BEZCIRCLE')

def register():
    bpy.utils.register_module(__name__)
    bpy.types.INFO_MT_add.append(custom_object_add)

def unregister():
    bpy.utils.unregister_module(__name__)
    bpy.types.INFO_MT_add.remove(custom_object_add)

if __name__ == "__main__":
    register()