**Core Concept**
Hyperparathyroidism is a disorder of calcium and phosphate metabolism caused by excess parathyroid hormone (PTH) secretion. The parathyroid glands regulate calcium levels by secreting PTH, which acts on various tissues to increase blood calcium levels.

**Why the Correct Answer is Right**
The most common cause of primary hyperparathyroidism is a solitary adenoma of one of the parathyroid glands. This adenoma leads to uncontrolled secretion of PTH, causing hypercalcemia and hyperparathyroidism. The adenoma is usually a benign tumor that arises from a parathyroid chief cell.

**Why Each Wrong Option is Incorrect**
* **Option A:** While hyperplasia is a cause of secondary hyperparathyroidism, it is not the most common cause of primary hyperparathyroidism.
* **Option B:** Familial hypocalciuric hypercalcemia (FHH) is a genetic disorder that causes hypercalcemia due to increased PTH secretion, but it is a rare cause of hyperparathyroidism.
* **Option C:** Parathyroid carcinoma is a rare cause of hyperparathyroidism and usually presents with more severe symptoms and higher PTH levels than a solitary adenoma.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the most common cause of primary hyperparathyroidism is a solitary adenoma, and it's often asymptomatic, making it a common diagnosis in patients with incidental hypercalcemia.

**Correct Answer: A. Solitary parathyroid adenoma.**