Identify the direction of opening,the coordinates of the center, the vertices, and the foci. Find the equations of the asymptotes and sketch the graph. x^2/16-y^2/9=1

Answer 1

x^2/16-y^2/9=1

a^2 = 16 ---> a = 4
b^2 = 9 ----> b = 3

centre: (0,0)
vertices: (-4,0), (4,0)
asympotes: y = ±(3/4)x

You should know the basic properties of a hyperbola in its standard form like this one.