**Core Concept**
The otic ganglion is a parasympathetic ganglion located near the foramen ovale in the infratemporal fossa. It plays a crucial role in the parasympathetic innervation of the parotid gland, which is involved in salivation. The parasympathetic supply to the otic ganglion is essential for the regulation of salivary secretion.

**Why the Correct Answer is Right**
The parasympathetic supply to the otic ganglion originates from the glossopharyngeal nerve (cranial nerve IX). The glossopharyngeal nerve carries preganglionic parasympathetic fibers that synapse in the otic ganglion. The postganglionic fibers from the otic ganglion then travel with the auriculotemporal nerve to innervate the parotid gland. This pathway is mediated by the neurotransmitter acetylcholine, which stimulates the muscarinic receptors in the parotid gland, leading to increased salivation.

**Why Each Wrong Option is Incorrect**
**Option A:** The facial nerve (cranial nerve VII) is responsible for the parasympathetic innervation of the submandibular and sublingual glands, not the parotid gland. Therefore, it is incorrect for the otic ganglion.
**Option B:** The vagus nerve (cranial nerve X) is involved in various parasympathetic functions, including the innervation of the pharynx and larynx, but it is not responsible for the parasympathetic supply to the otic ganglion.
**Option C:** The sympathetic supply to the parotid gland originates from the superior cervical ganglion, not the parasympathetic supply to the otic ganglion.

**Clinical Pearl / High-Yield Fact**
The otic ganglion is a small, bean-shaped ganglion located near the foramen ovale. It is an important landmark for surgeons performing parotid gland surgery, as damage to the ganglion can lead to facial paralysis and other complications.

**Correct Answer: C. The glossopharyngeal nerve (cranial nerve IX) is responsible for the parasympathetic supply to the otic ganglion.**