## College Algebra (6th Edition)

Fill the blanks with ... $(-5,0)$ ... $(5,0)$ ... ... $(-6,0)$ ... $(6,0)$ ...
The standard form of the equation of a hyperbola with center at the origin is $\displaystyle \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\ \$ the transverse axis lies on the x-axis or $\displaystyle \frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1 \ \$ the transverse axis lies on the y-axis. The vertices are $a$ units from the center and the foci are $c$ units from the center. For both equations, $b^{2}=c^{2}-a^{2}$. -------------- $\displaystyle \frac{x^{2}}{25}-\frac{y^{2}}{9}=1$ $a^{2}=25,\quad a=5$, the transverse axis lies on the x-axis. Vertices: $(-5,0)$ and $(5,0)$ $c^{2}=a^{2}+b^{2}$ $c^{2}=25+9=36$ $c=6$ Foci: $(-6,0)$ and $(6,0).$ Fill the blanks with ... $(-5,0)$ ... $(5,0)$ ... ... $(-6,0)$ ... $(6,0)$ ...