# How do you identify the vertices, foci, and direction of #x^2/81-y^2/4=1#?

##### 1 Answer

Please see the explanation.

#### Explanation:

The reference Conics: Hyperbolas tells us that the given equation:

is that of a hyperbola with a horizontal transverse axis. We can identify that the direction is horizontal, because the "x" term is positive and the "y" term is negative.

NOTE: If the "y" term were positive and "x" term were negative, then the direction would be vertical.

The reference, also, tells us that the following equation, [2], is the standard Cartesian form:

In this form, it is easy to observe or compute:

- The center is
#(h, k)# - The vertices are located at
#(h - a, k) and (h + a, k)# - The foci are located at
#(h - sqrt(a^2 + b^2), k) and (h + sqrt(a^2 + b^2), k)#

Write equation [1] in the form of equation [2]:

In this form, the vertices can be written by observation:

Compute

The foci are: