Hyperbolas

Definition

A set of all points in a plane such that the absolute value of the differences of the distance from the foci is constant.
Hyperbolas look like two parabolas opening in opposite directions. The equations of the asymptotes are y= k + (b/a)(x-h). The asymptotes help you to graph the hyperbola. The center of the hyperbola is also at (h, k). The vertices of the hyperbola depend on whether the hyperbolas open left and right or up and down. You can determine which way the hyperbola opens by looking to see if the x or y term has a negative sign. In the equation in the upper left corner the y term has the negative and since the y has the negative the hyperbolas open left and right. When opening left and right the vertices are (h+a, k). For the equation in the upper right corner the x value has the negative sign which means that the hyperbola opens up and down. The vertices for an equation that opens up and down are (h, k+b).