
### Instruction: help me answer this question Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbola 9y2 – 4x2 = 36, think step by step
### Assistant: Given the equation 9y2 – 4x2 = 36 or y2/4 – x2/9 = 1, we can compare it with the standard equation of a hyperbola y2/a2 – x2/b2 = 1. By doing so, we find that a = 2 and b = 3. We then calculate c using a2 + b2 = c2, which gives us c = √13. The coordinates , The answer is The coordinates of the foci are (0, √13) and (0, -√13), the coordinates of the vertices are (0, 2) and (0, -2), the eccentricity is e = c/a = √13/2, and the length of the latus rectum is (9/2).
