Write the equation of a hyperbola with vertices at (-3, 0) and (3, 0) and co-vertices (0, 5) and (0, -5).

Question

Write the equation of a hyperbola with vertices at (-3, 0) and (3, 0) and co-vertices (0, 5) and (0, -5).

Answer 1

The Midpoint of the Vertices is (0,0) the Center of the Hyperbola. And since they are located on a Horizontal Axis, then then general equation of the Hyperbola: x² / a² -- y² / b² = 1.

a = 3 (the distance from each Vertex to the Center)

b = 5 ( the distance from each Co-vertex to the Center)

And so the Equation of the Hyperbola is: x² / 9 -- y² / 25 = 1.