ページを更新せずにドロップダウンを更新するにはどうすればよいですか？

jQueryAjaxを使用する

yourfile.php

<select id="location" onchange="getState(this.value)" name="location" class='form-control'>
<option value="0">Select location</option>
    <?php
        $query = mysql_query("select * from city");
            while($row = mysql_fetch_assoc($query))
            {
                echo '<option value="'.$row['cityid'].'">'.$row['cityname']. '</option>';
            }
    ?>
</select>

<select id="state">

</select>

Jqueryスクリプト

function getState(city_id)
{
    var html = $.ajax({
        type: "POST",
        url: "path/to/ajax/my_ajax.php",
        data: "city_id=" +city_id,
        async: false
    }).responseText;
    if(html){
        $("#state").html(html);
    }
}

AJAX.php

$query = mysql_query("select * from state where city_id=".$_REQUEST['city_id']);
            while($row = mysql_fetch_assoc($query))
            {
                echo '<option value="'.$row['state_id'].'">'.$row['state_name']. '</option>';
            }