A320 pilot reported a hydraulic system failure during cruise. After consulting with maintenance and dispatch the flight continued to the destination where the post flight inspection confirmed a hydraulic fluid leak.

Narrative

While en-route from ZZZ Airport to ZZZ1 Airport north and east of ZZZ VOR at 34; 000 ft. an ECAM presented. Hyd y low pressure. The reservoir was empty according to the systems page. We applied the procedure and referenced the COM. The status page indicated that nose wheel steering would be unavailable. I then called Maintenance and Dispatch via ARINC. After conferring with and using all available information I requested priority handling. On approach the status page procedure had me select yellow hyd pump on. Although it was indicating 0 pressure in-flight once re-selected it produced 2950 PSI. We landed the aircraft on Runway XXR and were able to exit the runway and taxi to the gate. At this time the ECAM and status procedures were not presented. Emergency vehicles followed us to the gate where we parked and secured the aircraft. During post-flight a large puddle of what appeared to be hydraulic fluid was dripping and pooling under the #2 engine. Maintenance personnel boarded and started troubleshooting. I called the Chief Pilot on duty to inform the company of the actions that I had taken.