**Core Concept**
Achondroplasia is a genetic disorder that affects bone growth and development, leading to short stature and characteristic skeletal features. It is caused by mutations in a specific gene that encodes a crucial protein involved in bone formation.

**Why the Correct Answer is Right**
The correct answer is the FGFR3 gene, which codes for the fibroblast growth factor receptor 3. Mutations in this gene lead to the activation of the receptor, resulting in the inhibition of bone growth. Specifically, the mutations cause a gain-of-function in the receptor, leading to the decreased activity of the MAPK/ERK signaling pathway, which is essential for bone growth and development. The FGFR3 gene is a key regulator of bone growth, and mutations in this gene are responsible for the majority of cases of achondroplasia.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the FGFR1 gene is involved in other developmental processes and is not directly related to achondroplasia.
* **Option B:** This option is incorrect because the FGFR2 gene is also involved in other developmental processes and is not the primary cause of achondroplasia.
* **Option D:** This option is incorrect because the FGFR4 gene is involved in other cellular processes and is not directly related to achondroplasia.

**Clinical Pearl / High-Yield Fact**
Achondroplasia is the most common cause of short-limbed dwarfism, and it is estimated to affect 1 in 25,000 to 1 in 30,000 births. The FGFR3 gene is a critical regulator of bone growth, and mutations in this gene can lead to a range of skeletal abnormalities.

**Correct Answer: C. FGFR3 gene**