The transverse axis is parallel to the y-axis (the positive part of this equation.
(h, k) is the center ... (0, 0)
a = distance from the center to the vertices along the transverse axis
b = distance from the center to the endpoints of the conjugate axis
c = distance from the center to the foci along the transverse axis
Given: a = 10
The relationship between a, b, and c is
10² + b² = c²
The slope of the asymptotes is ±5/4
a = is a multiple of 5
b = is a multiple of 4 ... be careful not to always assume that a=5 and b = 4.
For this problem a = 10
hence, b = 8
10² + 8² = c²
164 = c²
2√41 = c
Summary
center = (0, 0)
a² = 100
b² = 64
c² = 164
transverse axis x = 0
equation of the hyperbola
[y²/10²] - [x²/8²] = 1
Remember, the slope of the asymptotes tell you the ratio of a and b, and not necessarily the actual values of a and b.
I hope this helps!
