Find the standard form equation for a hyperbola

Question

Find the standard form equation for a hyperbola with vertices at  and  and asymptote 

Answer 1

The vertices (a,0) and (-a,0) are along the x-axis, therefore the graph of hyperbola is open left and right and we use this standard equation form where x²/a² is dominant:

x²/a² - y²/b² =1

Center is at (0,0)

Asymptote to this is y= ±bx/a

Base on the properties, the following are given on the problem:

a=12

and the asymptote is y= ±bx/a = 34x

∴b/a = b/12 = 34

b=12(34)

b=408

So the equation of the hyperbola is:

x² /12² - y²/408² = 1