Given: Vertices are (± 6, 0) and one of the directrices is x = 4

To find: equation of the hyperbola

Formula used:

The standard form of the equation of the hyperbola is,

Vertices of the hyperbola are given by (±a, 0)

The equation of the directrices:

Vertices are (± 6, 0) and one of the directrices is x = 4

Therefore,

b² = a²(e² – 1)

⇒ b² = 45

The equation of hyperbola:

⇒ 5x² – 4y² = 180

⇒ 5x² – 4y² – 180 = 0

Hence, required equation of hyperbola is 5x² – 4y² – 180 = 0