**Core Concept**
The primary arterial supply to the nasal mucosa is crucial for understanding the pathophysiology of nasal hemorrhages, particularly in the context of surgery. The nasal mucosa receives its blood supply from branches of the external carotid artery, which is responsible for supplying blood to the external structures of the head and neck.

**Why the Correct Answer is Right**
The primary arterial supply to the nasal mucosa is provided by the sphenopalatine artery, a direct branch of the maxillary artery. The maxillary artery is a terminal branch of the external carotid artery, and it supplies blood to the nasal cavity, palate, and other structures in the face. The sphenopalatine artery arises from the maxillary artery and further divides into smaller branches that supply the nasal mucosa. Ligation of the sphenopalatine artery or its branches is a common surgical technique used to control nasal bleeding.

**Why Each Wrong Option is Incorrect**
**Option A:** The facial artery is a branch of the external carotid artery, but it primarily supplies the face, including the nose, but not the main nasal mucosa. It is not the primary arterial supply to the nasal mucosa.
**Option B:** The ophthalmic artery is a branch of the internal carotid artery and supplies the eye and adjacent structures, but it is not directly involved in supplying the nasal mucosa.
**Option C:** The superior labial artery is a branch of the facial artery and supplies the upper lip, but it is not the primary arterial supply to the nasal mucosa.

**Clinical Pearl / High-Yield Fact**
In cases of recurrent nasal hemorrhages, identifying and ligating the primary arterial supply to the nasal mucosa is crucial for controlling bleeding. The sphenopalatine artery is a key target for surgical intervention in these cases.

**Correct Answer: C. The maxillary artery.**