# How do you write an equation for the hyperbola with focus at (0, 25), asymptotes intersecting at (0, 5) and an asymptote passing through (24, 13)?

##### 1 Answer

Aug 31, 2016

#### Explanation:

The asymptotes intersect at the center

A focus is

where a is the semi transverse axis and e is the eccentricity.

The transverse axis is along the y-axis. So, the equation of the

hyperbola is

As it passes through (24, 13),

Substituting a = 20/e and simplifying,

As e > 1,

^Semi conjugate axis

And now, the equation is obtained as