How do you find the center and vertices and sketch the hyperbola $\frac{y^{2}}{9} - \frac{x^{2}}{1} = 1$ $y^2/9-x^2/1=1$ ?

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Answer 1 · 2017-01-06T22:15:42

Please see the explanation.

The center of a hyperbola with an equation of the general form:

$\frac{{(y - k)}^{2}}{a^{2}} - \frac{{(x - k)}^{2}}{b^{2}} = 1 [1]$ $(y - k)^2/a^2 - (x - k)^2/b^2 = 1" [1]"$

is the point $(h, k)$ $(h, k)$

In the given equation, h and k are obviously 0, therefore, the center is $(0, 0)$ $(0,0)$

Referring, again, to equation [1] the vertices are located at the points:

$(h, k - a) and (h, k + a)$ $(h, k -a) and (h, k + a)$

In the given equation, $a = 3$ $a = 3$ , therefore, the vertices are located at the points:

$(0, - 3) and (0, 3)$ $(0, -3) and (0, 3)$

Here is a graph of the hyperbola:

Desmos.com

How do you find the center and vertices and sketch the hyperbola y^2/9-x^2/1=1y29−x21=1y^2/9-x^2/1=1?