Given: Vertices are (±3, 0) and foci are (±5, 0)

To find: equation of the hyperbola

Formula used:

Standard form of the equation of hyperbola is,

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

Foci of hyperbola are given by (±ae, 0)

Vertices are (±3, 0) and foci are (±5, 0)

Therefore,

a = 3 and ae = 5

⇒ 3 × e = 5

b² = a²(e² – 1)

⇒ b² = 16

Equation of hyperbola:

⇒ 16x² – 9y² = 144

Hence, required equation of hyperbola is 16x² – 9y² = 144