Try below code to load product collection by category id

    $category_id = $this->getRequest()->getParam('cat'); // 10 as Category Id
    $products = Mage::getModel('catalog/category')->load($category_id)
        ->getProductCollection()
        ->addAttributeToSelect('*')
        ->addAttributeToFilter('status', 1) 
        ->addAttributeToFilter('visibility', 4)
        ->setOrder('price', 'ASC');