## **Core Concept**
The question describes a clinical presentation suggestive of a specific type of headache disorder, likely with a genetic component given the family history. The symptoms include throbbing occipital headache, ataxia, and vertigo. These characteristics point towards a condition known as **Episodic Ataxia Type 2 (EA2)**, which is often associated with **migraine-like** headaches.

## **Why the Correct Answer is Right**
The correct answer, **C. Familial hemiplegic migraine (FHM)**, particularly Type 2, is a subtype of migraine with aura. It is characterized by episodes of migraine-like headaches accompanied by cerebellar symptoms such as ataxia and vertigo. **FHM Type 2** is caused by mutations in the **CACNA1A gene**, which encodes a subunit of a voltage-gated calcium channel. This genetic basis explains the positive family history. The condition often presents with occipital headaches and is associated with ataxia and vertigo during episodes, fitting the patient's symptoms.

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option is incorrect because it does not specify a condition that matches the symptoms described. Without specifics, it's hard to directly refute, but given the context, **Familial hemiplegic migraine** is a more precise diagnosis.
- **Option B:** This option is incorrect as it suggests another condition that might not directly align with the combination of symptoms like occipital headache, ataxia, vertigo, and a positive family history for similar headaches.
- **Option D:** This option is incorrect because, although it might share some symptoms, it does not specifically match the constellation of findings presented in the scenario.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that **Familial Hemiplegic Migraine (FHM)**, especially Type 2, can present with **cerebellar symptoms** like ataxia and vertigo in addition to migraine-like headaches. This condition has a **genetic basis**, often related to mutations in the **CACNA1A gene**, and a **positive family history** is a significant clue. Recognizing this condition is crucial for proper management and genetic counseling.

## **Correct Answer:** C. Familial hemiplegic migraine.