Question

write the standard form equation of each hyperbola:

vertices: (1,9), (1, -15)
endpoints of conjugate axis: (14, -3), (-12,-3)

Answer 1

vertices along line x=1 implying vertical hyperbola
2a = |-15-9| = 24
a = 12
a^2 = 144
conjugate axis along y=-3
2b = |-12-14| = 26
b=13
b^2 = 169
center (1,-3)

\[\frac{(y+3)^{2}}{144} - \frac{(x-1)^{2}}{169} = 1\]