Java: draw an Ellipse2D starting from the coordinates of the two foci

Ellipse2D allows me to draw an ellipse assuming I know coordinates of the top-left corner, and the a and b axes. Instead, I have the coordinates of the two foci, and the l distance of each point from the two foci. How can I create the corresponding Ellipse2D starting from the coordinates of the two foci?

Here is my code. It creates an ellipse of the right size centred on the origin (0,0). It then uses an AffineTransform to translate and rotate the ellipse to the proper place. Returns a Shape that defines the required ellipse. The variable names come from http://math.tutorvista.com/geometry/ellipse-equation.html Hope it works for you.

   #import java.awt.geom.*;

   /* Create an ellipse given foci and distance. 
     (x1,y1) and (x2,y2) are  foci. semimajor axis (the sum of distances
     that define the ellipse) is *dist*.
     See
     for meaning of vars
   */
    public Shape makeEllipse (
        float x1, float y1, float x2, float y2, float dist
    )
    {
        // Create foci points
        Point2D f1 = new Point2D.Float (x1, y1);
        Point2D f2 = new Point2D.Float (x2, y2);

        // Calculate ellipse characteristics
        double a = dist / 2.0;
        double c = f1.distance (f2) / 2.0;
        // If 'dist' is smaller than the distance between foci, 
        // the ellipse is invalid
        if (a < c)
           die ("Invalid semimajor axis length"); 
        double b = Math.sqrt (a * a - c * c);

        Point2D centre = 
            new Point2D.Float ((x1 + x2) / 2.0, (y1 + y2) / 2.0);

        // Create a transform to rotate and translate the ellipse
        double theta = Math.atan2 (y2 - y1, x2 - x1);
        AffineTransform trans = new AffineTransform();
        trans.translate (centre.getX(), centre.getY());
        trans.rotate(theta);

        // Create an ellipse with correct size but origin at centre 
        Ellipse2D tmpEllipse = new Ellipse2D.Double (-a, -b, 2 * a, 2 * b);

        // Translate and rotate it to where it should be
        Shape ellipse = trans.createTransformedShape (tmpEllipse);

        return ellipse;
    }