Math Snap

STEP 1

Assumptions1. The given equation is of a hyperbola. The equation is in the standard form $\frac{y^{}}{a^{}} - \frac{x^{}}{b^{}} =1$
3. The center of the hyperbola is at the origin (0,0)

STEP 2

From the given equation, we can identify the values of $a^{2}$ and $b^{2}$. Here, $a^{2} =16$ and $b^{2} =1$.

STEP 3

To find the values of a and b, we take the square root of $a^{2}$ and $b^{2}$.
$$a = \sqrt{16} =$$$$b = \sqrt{1} =1$$

STEP 4

The asymptotes of the hyperbola are given by the equations $y = \pm \frac{a}{b}x$.

STEP 5

Substitute the values of a and b into the equations for the asymptotes.
$$y = \pm \frac{4}{1}x$$$$y = \pm4x$$

STEP 6

The equations of the asymptotes of the hyperbola are $y =4x$ and $y = -4x$.

STEP 7

To graph the hyperbola, we need to plot the center, vertices, and asymptotes.The center is at the origin (0,0).The vertices are at (0,4) and (0,-4) because the hyperbola opens upwards and downwards as the y-term is positive in the equation.The asymptotes are the lines $y =4x$ and $y = -4x$.

Draw the graph of the hyperbola using the information from the previous step.