Update.php

<?php
if (!empty($_GET['id']) && !empty($_GET['value'])) {

    $id = $_GET['id'];
    $value = $_GET['value'];

    try {

        $objDb = new PDO('mysql:host=localhost;dbname=cars', 'root', 'janix93');
        $objDb->exec('SET CHARACTER SET utf8');

        $sql = "SELECT *
                FROM `categories`
                WHERE `master` = ".$value;
        $statement = $objDb->prepare($sql);
        $statement->execute(array($value));
        $list = $statement->fetchAll(PDO::FETCH_ASSOC);

        if (!empty($list)) {

            $out = array('<option value="">Select one</option>');

            foreach($list as $row) {
                $out[] = '<option value="'.$row['id'].'">'.$row['name'].'</option>';
            }

            echo json_encode(array('error' => false, 'list' => implode('', $out)));

        } else {
            echo json_encode(array('error' => true));
        }

    } catch(PDOException $e) {
        echo json_encode(array('error' => true));
    }

} else {
    echo json_encode(array('error' => true));
}

?>