Find an equation for the hyperbola with vertices at (0, -6) and (0, 6);

Question

asymptote the line y =3/5x?

Answer 1

The vertices are (0,-6) and (0,6)

The asymptote is y=(3/5)x

Here the vertices are in the form of (0, ±a)   that is (0,±6).

So, it is vertical hyperbola and the equation for vertical hyperbola is .

Here a = 6 and from the asymptote line equation m = 3/5.

m= a / b =6 / b = 3/5.

Hence, b= 10.

So,the equation for the hyperbola is .

Hence the equation of hyperbola is .