1 Answer

IFanie · Answer 1 · 2023-01-09T22:21:26+0000

Given

The equation of the hyperbola is:

$(y^2)/(9)\text{ -x}^2\text{ = 1}$

We can see that this is a vertical hyperbola since y is positive.

The general equation of a vertical hyperbola is:

$\begin{gathered} ((y-k)^2)/(a^2)\text{ -}\frac{(x\text{ -h})^2}{b^2}=\text{ 1} \\ Where\text{ }(h,k)\text{ is the center} \end{gathered}$

The steps to graph a hyperbola are:

1. Determine if it is horizontal or vertical. Find the center point, a, and b.

2. Graph the center point.

3. Use the a value to find the two vertices.

4. Use the b value to draw the guiding box and asymptotes.

5. Draw the hyperbola.

Step 1: This hyperbola is vertical

center point = (0,0)

Step 2: The values of a and b

$\begin{gathered} a^2=\text{ 9} \\ a\text{ = 3} \\ b^2\text{ = 1} \\ b\text{ = 1} \end{gathered}$

Step 3: Draw the guiding box:

Step 4: Draw the asymptotes

The asymptotes are diagonal lines through the corners of the box

Step 5: Finally, we draw in our hyperbola. Each half starts at the vertex and continues towards the asymptotes but never actually reaches them.

Step 6:

The center point, guiding box, and asymptotes are not technically part of the answer, so a clean version of the graph would look like this:

The graph of the hyperbola is shown below:

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