Final answer:
The equation of the given ellipse is x²/25 + y²/64 = 1.
Step-by-step explanation:
The equation of the ellipse given the center at (0,0), vertex at (0,8), and b = 5 is:
x²/25 + y²/64 = 1
To determine the equation of an ellipse, we use the standard form equation: (x - h)²/a² + (y - k)²/b² = 1, where (h,k) represents the center of the ellipse, a represents the distance from the center to the vertices in the horizontal direction, and b represents the distance from the center to the vertices in the vertical direction.
In this case, the center is (0,0), a = 5, and b = 8. Substituting these values into the equation, we get (x - 0)²/5² + (y - 0)²/8² = 1. Simplifying, we get x²/25 + y²/64 = 1.
Learn more about Ellipse here: