Drupal search based on content type
You could make the same search with a view and add contextual filter to achieve the specific URL pattern and normal field filters to apply other filtration if needed. The view could render the node with the same display that you was going to use for the default search so if you have already built the markup - you don't have to do it again.

Edit:
Also if you want to use the default search api - you could make a facet to filter with the help of the Facet API Module