# How do you identify the vertices, foci, and direction of y^2/9-x^2/25=1?

May 16, 2017

Vertices: $\left(0 , \pm 3\right)$
Foci: $\left(0 , \pm \sqrt{34}\right)$
Direction: along $y$-axis

#### Explanation:

The vertices are $\pm a$ from the origin along the $y$-axis $= \left(0 , 3\right)$ and $\left(0 , - 3\right)$ (it's along the $y$-axis because $y$ is over the $a$ part of the equation).

The foci of the hyperbola are

$\left(0 , \pm c\right)$

where ${c}^{2} = {a}^{2} + {b}^{2}$

${c}^{2} = {\left(3\right)}^{2} + {\left(5\right)}^{2}$

$c = \pm \sqrt{34}$

So the foci are

$\left(0 , \sqrt{34}\right)$ and $\left(0 , - \sqrt{34}\right)$