Facebook Login from an external site

I have a Facebook application on my site. When we integrate Facebook, it will lead to facebook login page every time, but I want to login to facebook from mysite. I will give a separate facebook login form, when we enter facebook, critical in mysite login, it will login to facebook without asking facebook login page. Can this be done? I am trying to perform the following curl function but fail

<?php

$EMAIL      = "fb_user_email";
 $PASSWORD   = "password";

  function cURL($url, $header=NULL, $cookie=NULL, $p=NULL)
  {
      $ch = curl_init();
      curl_setopt($ch, CURLOPT_HEADER, $header);
      curl_setopt($ch, CURLOPT_NOBODY, $header);
      curl_setopt($ch, CURLOPT_URL, $url);
      curl_setopt($ch, CURLOPT_SSL_VERIFYHOST, 0);
      curl_setopt($ch, CURLOPT_COOKIE, $cookie);
      curl_setopt($ch, CURLOPT_USERAGENT, $_SERVER['HTTP_USER_AGENT']);
      curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
      curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, 0);
      curl_setopt($ch, CURLOPT_FOLLOWLOCATION, 1);
      if ($p) {
         curl_setopt($ch, CURLOPT_CUSTOMREQUEST, "POST");
         curl_setopt($ch, CURLOPT_POST, 1);
         curl_setopt($ch, CURLOPT_POSTFIELDS, $p);
       }
       $result = curl_exec($ch);
       if ($result) {
          return $result;
        }
        else {
          return curl_error($ch);
        }
        curl_close($ch);
    }

$a = cURL("https://login.facebook.com/login.php?login_attempt=1",true,null,"email=$EMAIL&pass=$PASSWORD");
preg_match('%Set-Cookie: ([^;]+);%',$a,$b);
$c = cURL("https://login.facebook.com/login.php?login_attempt=1",true,$b[1],"email=$EMAIL&pass=$PASSWORD");
preg_match_all('%Set-Cookie: ([^;]+);%',$c,$d);
for($i=0;$i<count($d[0]);$i++)
$cookie.=$d[1][$i].";";


echo cURL("http://graph.facebook.com/oauth/authorize?client_id=APP_IDredirect_uri=APP_REDIRECT_URL&display=touch&scope=publish_stream, user_checkins, publish_checkins, offline_access",null,$cookie,null);
?>

Please help me do this. This is my task

Thanks in advance