Question

Find the vertices and foci of the hyperbola (y² / 9) - (x² / 16) = 1

a) Vertices: (0, ±3), Foci: (0, ±5)
b) Vertices: (0, ±5), Foci: (0, ±3)
c) Vertices: (0, ±4), Foci: (0, ±5)
d) Vertices: (0, ±5), Foci: (0, ±4)

Answer 1

The vertices of the hyperbola are (±3, 0) and the foci are (±5, 0).

Step-by-step explanation:

The given equation represents a hyperbola in the form (y² / a²) - (x² / b²) = 1. Comparing this with the given equation (y² / 9) - (x² / 16) = 1, we can see that a² = 9 and b² = 16. Therefore, a = 3 and b = 4.

The vertices of a hyperbola are given by (±a, 0), which in this case are (±3, 0). The foci of a hyperbola are given by (±c, 0), where c = √(a² + b²). Substituting the values of a and b, we get c = √(9 + 16) = √25 = 5. Therefore, the foci are (±5, 0).