The equation (y^2)/(8^2)−(x^2)/(b^2)=1 represents a hyperbola centered at the origin with a focus of open paren 0 comma negative 10 close paren What is the value of b ?

For a hyperbola of the form y²/a² − x²/b² = 1, the focus distance satisfies c² = a² + b². Here a = 8 and c = 10, so b² = 10² − 8² = 100 − 64 = 36, giving b = 6. The correct choice is 6.

AI-written and checked against the verified answer.