The relation between p and q such that the point (p, q) is equidistant from (–4, 0) and (4, 0) is

Formula used:

Let the point be A (p, q), B (–4, 0) and C (4, 0)

Distance of AB

⇒ AB = √ (–4 – p)² + (0 – q)²)

⇒ AB = √ ((–4 – p)² + (–q)²)

⇒ AB = √ (16 + p² + 8p + q²)

Distance of AC

⇒ AC = √ (4 – p)² + (0 – q)²)

⇒ AC = √ ((4 – p)² + (–q)²)

⇒ AC = √ (16 + p² – 8p + q²)

i.e. AB = AC (Given)

⇒ 16 + p² + 8p + q² = 16 + p² – 8p + q²

Squaring both sides

⇒ 16 + p² + 8p + q² = 16 + p² – 8p + q²

⇒ 16 + p² + 8p + q² – 16 – p² + 8p – q² = 0 …

⇒ 16 p = 0

⇒ p = 0

∴ Option A is correct.