# How do you find the vertices, asymptote, foci and graph y^2/25-x^2/49=1?

Dec 13, 2016

#### Explanation:

The standard form for the equation of a hyperbola with a vertical transverse axis is:

${\left(y - k\right)}^{2} / {a}^{2} - {\left(x - h\right)}^{2} / {b}^{2} = 1$

The center is: $\left(h , k\right)$
The vertices are: $\left(h , k - a\right) \mathmr{and} \left(h , k + a\right)$
The foci are: $\left(h , k - \sqrt{{a}^{2} + {b}^{2}}\right) \mathmr{and} \left(h , k + \sqrt{{a}^{2} + {b}^{2}}\right)$
The equations of the asymptotes are:
$y = - \frac{a}{b} \left(x - h\right) + k \mathmr{and} y = \frac{a}{b} \left(x - h\right) + k$

Write the given equation in this form:

${\left(y - 0\right)}^{2} / {5}^{2} - {\left(x - 0\right)}^{2} / {7}^{2} = 1$

The center is: $\left(0 , 0\right)$
The vertices are: $\left(0 , - 5\right) \mathmr{and} \left(0 , 5\right)$
The foci are: $\left(0 , - \sqrt{74}\right) \mathmr{and} \left(0 , \sqrt{74}\right)$
The equations of the asymptotes are:
$y = - \frac{5}{7} x \mathmr{and} y = \frac{5}{7} x$

Here is the graph: