Magento query to check for product visible or visibility and enable or is_enable

Magento query to check for product visible or visibility and enable or is_enable

$visibility = array(Mage_Catalog_Model_Product_Visibility::VISIBILITY_BOTH,Mage_Catalog_Model_Product_Visibility::VISIBILITY_IN_CATALOG);
$prod= Mage::getModel('catalog/product')->getCollection();
->addAttributeToFilter('visibility', $visibility);
->addAttributeToFilter('status', Mage_Catalog_Model_Product_Status::STATUS_ENABLED);