# Finding the Key Parts of All Hyperbolas

### Part of the Pre-Calculus Workbook For Dummies Cheat Sheet

A *hyperbola* is the set of all points in the plane such that the difference of the distances from two fixed points (the *foci*) is a positive constant. Hyperbolas always come in two parts, and each one is a perfect mirror reflection of the other. There are horizontal and vertical hyperbolas, but regardless of how the hyperbola opens, you always find the following parts:

The center is at the point (

*h, v*).The graph on both sides gets closer and closer to two diagonal lines known as

*asymptotes.*The equation of the hyperbola, regardless of whether it's horizontal or vertical, gives you two values:*a*and*b.*These help you draw a box, and when you draw the diagonals of this box, you find the asymptotes.There are two axes of symmetry:

The one passing through the

*vertices*is called the*transverse axis.*The distance from the center along the transverse axis to the vertex is represented by*a.*The one perpendicular to the transverse axis through the center is called the

*conjugate axis.*The distance along the conjugate axis from the center to the edge of the box that determines the asymptotes is represented by*b.**a*and*b*have no relationship;*a*can be less than, greater than, or equal to*b.*

You can find the foci by using the equation

*f*^{2}=*a*^{2}+*b*^{2}.