procedure TForm1.EllipseAngle(ACanvas: TCanvas; XCenter, YCenter,
 XRadius, YRadius: Integer; Angle: Integer);
const
 Step = 49;
var
 RX, RY: Integer;
 i: Integer;
 Theta: Double;
 SAngle, CAngle: Double;
 RotAngle: Double;
 XC, YC: Integer;
 Kf: Double;
 X, Y: Double;
 XRot, YRot: Integer;
 Points: array[0..Step] of TPoint;
begin
 RotAngle := Angle * PI / 180;
 Kf := (360 * PI / 180) / Step;
 SAngle := Sin(RotAngle);
 CAngle := Cos(RotAngle);
 for i := 0 to Step do
 begin
  Theta := i * Kf;
  X := XCenter + XRadius * Cos(Theta);
  Y := YCenter + YRadius * Sin(Theta);
  XRot := Round(XCenter + (X - XCenter) * CAngle - (Y - YCenter) * SAngle);
  YRot := Round(YCenter + (X - XCenter) * SAngle + (Y - YCenter) * CAngle);
  Points[i] := Point(XRot, YRot);
 end;
 ACanvas.Polygon(Points);
end;

procedure RotatedEllipse(aCanvas: TCanvas; X1, Y1, X2, Y2: Integer);
var
 T, O: TXForm; {in unit Windows}
begin
 { ... }
 SetGraphicsMode(aCanvas.Handle, GM_Advanced);
 GetWorldTransform(aCanvas.Handle, O);
 {Angle in degree}
 T.eM11 := 1 * Cos(w / 360 * Pi * 2);
 T.eM22 := 1 * Cos(w / 360 * Pi * 2);
 T.eM12 := 1 * Sin(w / 360 * Pi * 2);
 T.eM21 := 1 * -Sin(w / 360 * Pi * 2);
 T.eDX := Round((X1 + X2) / 2);
 T.eDY := Round((Y1 + Y2) / 2);
 ModifyWorldTransform(aCanvas.Handle, T, MWT_LEFTMULTIPLY);
 Canvas.Ellipse(X1, Y1, X2, Y2);
 SetWorldTransform(TheDraw.Handle, O);
end;