What is the equation for a hyperbola with transverse axis of length 24 and centered at the origin?

Answer 1

The standard form of the equation of a hyperbola with center at the origin is

x2/a2 - y2/b2 = 1 where the transverse axis lies on the x-axis,

or

y2/a2 - x2/b2 = 1 where the transverse axis lies on the y-axis.

The vertices are a units from the center and the foci are c units from the center.

For both equations, b2 = c2 - a2. Equivalently, c2 = a2 + b2.

Since we know the length of the transverse axis (the distance between the vertices), we can find the value of a (because the center, the origin, lies midway between the vertices and foci).

Suppose that the transverse axis of our hyperbola lies on the x-axis.

Then, |a| = 24/2 = 12

So the equation becomes x2/144 - y2/b2 = 1.

To find b we need to know what c is.