Find the vertices and asymptotes of the hyperbola.

Question

Quizplus · Accepted Answer

The hyperbola has a horizontal transverse axis, which means the vertices are located on the horizontal axis and the asymptotes are vertical. This rules out choices A, B, and D. 
The distance between the vertices is given by 2a, and in this case, it is equal to 6. Therefore, a = 3. 
The value of b can be found using the equation b^2 = c^2 - a^2, where c is the distance from the center to each focus (which is not given in the question). However, since we know that the asymptotes are located at y = k ± (b/a)x, and the slope of the asymptotes is ±b/a, we can use this information to find the value of b/a. From the given asymptotes, we see that b/a = 1, so b = a = 3. 
Therefore, the vertices are located at (0, ±3), which matches choice E.

Find the Vertices and Asymptotes of the Hyperbola