Find the standard form of the equation of the hyperbola sati

Find the standard form of the equation of the hyperbola satisfying the given conditions. Endpoints of transverse axis: (0, -10), (0,10); asymptote: y =5/8 x

Solution

centre=(0,0)

transverse axis is the distance between the vertices i.e 20.

therefore, a=20/2=10.

a/b = 5/8

=> b = 8*10/5 = 16

therefore equation of hyperbola is [y/(10^2) - x/(16^2)] =1