Question

What are the coordinates of the vertices of the hyperbola?

Answer 1

The vertices of the hyperbola are at (-9, 5) and (1, 5).

Step-by-step explanation:

The vertices of a hyperbola are always aligned in the center of the hyperbola.

Based on the equation, we can easily see that the center of the hyperbola is at (-4, 5). We got the center by equating the numerator into zero and solving x and y.

`\begin{gathered} x+4=0\Rightarrow x=-4 \\ y-5=0\Rightarrow y=5 \end{gathered}`

Between the x and y variables in the equation of the hyperbola, the x-variable is positive. Hence, we have a horizontal hyperbola.

Since it is a horizontal hyperbola, the distance between the two vertices and the center is √25 or just 5 units horizontally. We will add and subtract 5 on the coordinates of the center.

`\begin{gathered} (-4+5,5)\Rightarrow(1,5) \\ (-4-5,5)\Rightarrow(-9,5) \end{gathered}`

Hence, the vertices of the hyperbola are located at (-9 5) and (1, 5).