Identify the equation or coordinates of the following conic and its equation. find the equations for the asymptotes of the hyperbola.

x^2/36 - y^2/5 = 1

Hyperbola equation:

(x-h)²/a² - (y-k)²/b² =1
In our case h & k = 0 & the equation become x²/a² - y²/b² =1
==> x²/36 p- y²/25 =1 (with a=6  &   b=5)
1) since a>b==> the hyperbola opens right & left
2) The formula of the asymptotes is y₁=k+b/a(x-h) & y₂=k-b/a(x-h)
Since h=k=0 then the equations of the hyperbola are y₁=(6/5)x & y₂=(-6/5)x

Yes, two vertical lines can be complementary