function value = ellipse_area1 ( a, r )

%*****************************************************************************80
%
%% ellipse_area1() returns the area of an ellipse defined by a matrix.
%
%  Discussion:
%
%    The points X in the ellipse are described by a 2 by 2
%    positive definite symmetric matrix A, and a "radius" R, such that
%      X' * A * X <= R * R
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    08 November 2016
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    real A(2,2), the matrix that describes the ellipsoid.  
%    A must be symmetric and positive definite.
%
%    real R, the "radius" of the ellipse.
%
%  Output:
%
%    real VALUE, the area of the ellipse.
%
  value = r * r * pi / sqrt ( a(1,1) * a(2,2) - a(2,1) * a(1,2) );

  return
end
