Question

Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ±5/6x.

Answer 1

Standard form equation of hyperbola is:
y² / a² + x² / b² = 1
Vertices are: ( 0, a ) and ( 0, - a ) so :  a = 10
Asymptotes are : y = +/- a/b x
a/b = 5/6
10/b = 5/6
5 b = 60
b = 60 : 5
b = 12
Answer:
y² / 100 + x² / 144 = 1