How do you identify the vertices, foci, and direction of #x^2/81-y^2/4=1#?
Please see the 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, , is the standard Cartesian form:
In this form, it is easy to observe or compute:
- The center is
- 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  in the form of equation :
In this form, the vertices can be written by observation:
The foci are: