Rotate camera with player

I'm using the MouseOrbitImproved script and it more or less does what I want it to do but I need help implementing one more thing.

When the player runs to the right or left, I would like the camera to follow him around in a circle, similar to in most platform games.

What's the best way to achieve this? Here's the Mouse Orbit code

 void LateUpdate()
     {
         if (target)
         {
             x += Input.GetAxis("Mouse X") * xSpeed * distance * 0.02f;
             y -= Input.GetAxis("Mouse Y") * ySpeed * 0.02f;
 
             y = ClampAngle(y, yMinLimit, yMaxLimit);
 
             RaycastHit hit;
             if (Physics.Linecast(target.position, transform.position, out hit))
             {
                 distance -= hit.distance;
             }
 
             distance = Mathf.Clamp(distance - Input.GetAxis("Mouse Y") * 0.1f, distanceMin, distanceMax);
 
             Quaternion rotation = Quaternion.Euler(y, x, 0);
 
             Vector3 negDistance = new Vector3(0.0f, 0.0f, -distance);
             Vector3 position = rotation * negDistance + target.position;
 
             transform.rotation = rotation;
             transform.position = position;
         }
     }