If e₁ is the eccentricity of the ellipse x²/16 + y²/25 = 1 and e₂ is the eccentricity of the hyperbola passing through the foci of the ellipse and e₁e₂ = 1, then the equation of the hyperbola is:
a) x²/25 - y²/16 = 1
b) x²/16 - y²/25 = 1
c) x²/25 - y²/16 = -1
d) x²/16 - y²/25 = -1