Equation of hyperbola

Question

Write an equation of the hyperbola given that the transverse axis is vertical and is 6 units and the central rectangle is 6 units by 4 units.

Answer 1

"Transverse axis is vertical"
Equation of a vertical hyperbola
y²/a² - x²/b² = 1

"Transverse axis is vertical and is 6 units"
length of transverse axis = 2a = 6
a = 3

"central rectangle is 6 by 4 units"
length of conjugate axis = 2b = 4
b = 2

y²/3² - x²/2² = 1