**Core Concept**
The question is testing the understanding of the pathophysiology of hyperparathyroidism, particularly the effects of elevated calcium levels on the body. Hyperparathyroidism is characterized by the excessive production of parathyroid hormone (PTH), leading to hypercalcemia. The kidneys play a crucial role in regulating calcium levels by adjusting the excretion of calcium in the urine.

**Why the Correct Answer is Right**
The extensive calcium deposits in the lungs and kidney parenchyma are best explained by the mechanism of **calcification**. In hyperparathyroidism, the elevated calcium levels cause an increase in the calcium content of the blood. The kidneys, in an attempt to eliminate the excess calcium, increase the excretion of calcium in the urine. However, some of the excess calcium is deposited in various tissues, including the lungs and kidney parenchyma, leading to calcification. This process is facilitated by the presence of calcium phosphate, which is deposited in the tissues as calcium phosphate crystals.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is not relevant to the pathophysiology of hyperparathyroidism and the deposition of calcium in tissues.

**Option B:** This option is incorrect because it does not accurately describe the mechanism of disease. While hyperparathyroidism can lead to renal failure, the extensive calcium deposits in the lungs and kidney parenchyma are not a direct result of renal failure.

**Clinical Pearl / High-Yield Fact**
In hyperparathyroidism, the kidneys play a crucial role in regulating calcium levels, and an increase in the excretion of calcium in the urine can lead to the deposition of calcium in various tissues, including the lungs and kidney parenchyma.

**Correct Answer:** C.