Final answer:
The standard form of the equation of a hyperbola with given foci and vertices is y²/36 - x²/64 = 1.
Step-by-step explanation:
The standard form of the equation of a hyperbola with foci and vertices on the y-axis can be written as:
(y - k)²/a² - (x - h)²/b² = 1
Where (h, k) are the coordinates of the center of the hyperbola, a is the distance from the center to each vertex, and b is the distance from the center to each focus.
In this case, the center is (0, 0), the distance from the center to each vertex is 6, and the distance from the center to each focus is 8. Therefore, the standard form of the equation is:
y²/36 - x²/64 = 1