AJAX - peticion ajax sin enviar datos

function objetoAjax(){

    var xmlhttp=false;

    try {

        xmlhttp = new ActiveXObject("Msxml2.XMLHTTP");

    } catch (e) {

	    try {

	        xmlhttp = new ActiveXObject("Microsoft.XMLHTTP");

	    } catch (E) {

	        xmlhttp = false;

	    }

	}

	if (!xmlhttp && typeof XMLHttpRequest!='undefined') {

	    xmlhttp = new XMLHttpRequest();

    }

    return xmlhttp;

}

ajax=objetoAjax();

ajax.open("ultimo_registro.php",true);

ajax.onreadystatechange=function() {

    if (ajax.readyState==4) {

        //se supone aqui obtengo el dato del ultimo registro

        var ultimo_id = ajax.responseText

        alert(ultimo_id)

    }

}

<?php

require 'conectar_bd.php';

$consulta = mysql_query("SELECT * FROM solicitudes ORDER BY id DESC LIMIT 1") or die('Error. '.mysql_error());

$resultado = mysql_fetch_array($consulta);

echo $resultado['id'];

?>

ajax=objetoAjax();

ajax.open("GET","ultimo_registro.php",true);

ajax.onreadystatechange=function() {

    if (ajax.readyState==4 && this.status==200) {

        //se supone aqui obtengo el dato del ultimo registro

        var ultimo_id = ajax.responseText

        alert(ultimo_id);

    }

}

function  objetoAjax(){

    /*Se comprueba si el navegador es compatible*/

    var activexmodes=["Msxml2.XMLHTTP", "Microsoft.XMLHTTP"]

    //activeX versions to check for in IE

    if (window.ActiveXObject)

    {

        //Test for support for ActiveXObject in IE first (as XMLHttpRequest in IE7 is broken)

        for (var i=0; i<activexmodes.length; i++){

	        try{

	            return new ActiveXObject(activexmodes[i])

	        } catch(e){

	            //suppress error

	        }

        }

    } else if (window.XMLHttpRequest) // if Mozilla, Safari etc

        return new XMLHttpRequest()

    else

        return false

}