How do you write the equation for a hyperbola given vertices (-5,0) and (5,0), conjugate axis of lengths 12 units?
Please see the explanation for steps leading to the equation:
The two vertices have the same y coordinate, therefore, the hyperbola is the horizontal transverse axis type. The standard equation for the horizontal transverse axis type is:
We know that the general form for the vertices of this type are:
Using the given vertices
Solve for h and a:
From the reference, the length of the conjugate axis is equal to 2b:
We know the values of h, k, a, and b, substitute them into the general form: