Question

X²/⁹ - y²/⁴ = 1 the vertices of the hyperbola are (±3, 0) (0, ±3) (±2, 0)

Answer 1

The given equation represents a hyperbola with vertices at (±3, 0) and (0, ±3) and (±2, 0). The center of the hyperbola is (0,0) and the values of a and b are 3 and 2 respectively.

Step-by-step explanation:

The equation given, x²/⁹ - y²/⁴ = 1, represents a hyperbola. The vertices of the hyperbola are the points (±3, 0) and (0, ±3) and (±2, 0)

For a hyperbola in the standard form (x-h)²/a² - (y-k)²/b² = 1, the center of the hyperbola is the point (h, k). The values of a and b determine the shape and size of the hyperbola, with a being the distance from the center to the vertices along the x-axis, and b being the distance from the center to the vertices along the y-axis.

So, in this case, the center of the hyperbola is (0,0) and the values of a and b are 3 and 2 respectively.