QuestionDetermine the center, vertices, foci, and axis of the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and graph it.

Studdy Solution
To graph the hyperbola, plot the center, vertices, and foci on the coordinate plane. Draw the hyperbola opening up and down with vertices at $(0, -4)$ and $(0,4)$ and foci at $(0, -\sqrt{17})$ and $(0, \sqrt{17})$. The asymptotes of the hyperbola are the lines $y = \pm \frac{a}{b}x = \pm4x$.
The center, vertices, foci, and axis of the hyperbola given by the equation $\frac{y^{}}{16}-x^{}=$ are $(0,0)$, $(0, -4)$ and $(0,4)$, $(0, -\sqrt{17})$ and $(0, \sqrt{17})$, and $x =0$ respectively.