Question

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin.

Foci: (0, ±8);    asymptotes: y = ±4x

Answer 1

step 1:

The  foci of hyperbola : and asymptotes are : .

The standard form of hyperbola is .

Asymptotes of hyperbola are : .

Compare the asymptotes :

Centre .

slope of the asymptotes

step 2:

The distance from the origin to either foci is .

The value of [ from the foci ] .

From the hyperbola definition : .

Substitute the values of center , in standard form.

Solution :

.