Find the asymptotes of the hyperbola

Question

y²/4 - (x-2)²/9 = 1

Answer 1

Greetings! Lets solve this shall we ?

So, we must find the equations of the asymptotes given this hyperbola! By the way the equation is set up, I see we have a vertical hyperbola where

a² = 4 and b² = 9. Then a = 2 and b = 3, right ? Also, h = 2 and k = 0 from the vertex of the hyperbola.

The equations of asymptotes are as follows:

y = (b/a)(x-h) + k and y = (-b/a)(x-h) + k.......All we do now is plug in the information we found to obtain

y = (3/2)(x-2) and y = (-3/2)(x-2)

I hope this helped!