what is the equation of a hyperbola with one vertex at (6,5) and the equation of asymptotes are 5x-6y-30 and 5x+6y-30?

Answer 1

I will assume that you meant the asymptotes to be
5x+6y = 30 and 5x-6y=30

We know that the asymptotes intersect at the centre of the hyperbola.
Solving these I got (6,0)

The general equation of the asymptote is bx ± ay = k
so we can also see that a=6 and b=5, which would correctly give us one of the vertices at (6,5)

by making a sketch we can also see that the major axis is parallel to the y - axis.

So now the equation can be stated as

(x-6)^/36 - y^2/25 = -1