Answer:
y²/324 -x²/36 = 1
Step-by-step explanation:
Where (0, ±b) are the ends of the transverse axis and y = ±(b/a)x describes the asymptotes, the equation of the hyperbola can be written as ...
y²/b² -x²/a² = 1
Application
Here, we have transverse axis endpoints of (0, ±18) and asymptotes of y = ±3x, so we can conclude ...
b = 18
b/a = 3 ⇒ a = 18/3 = 6
The equation of the hyperbola in standard form is ...
y²/324 -x²/36 = 1
