Find the equation of this hyperbola with the given information?

Question

Hey, I am having problems with this math problem.
Here's the given Info.
Hyperbola: foci (2,1) and (8,1), conjugate axis is 6 units.

Here's what I worked out:
The center is (5,1) since its right in the middle of the foci.
And in terms of "a" "b" and "c", the formula would be a^2 + b^2 = c^2
So b=3 and c=3.
If I have worked it out right, here's what I get:
a^2+3^2=3^2
a^2 = 9 - 9
a^2 = 0
a = 0
Since a is zero, where would the asymptotes be?
You dont have to do ALL the work, just enough so I can see where the asymptotes would be. First person who explains it to me gets 10 points.

Answer 1

Hyperbola: foci (2,1) and (8,1), conjugate axis is 6 units
The center of the hyperbola is located at (5,1) So it's equation takes the form of: [(x-5)^2]/a^2 - [(y-k)^2]/b^2 = 1Since Since the conjugate axis is 6, then b= 3. c = (8-2)2=3. So a = 0 which means the vertices of the two branches touch each other. It also means that the above equation has a denominator that is equal to zero. It also means the asymptotes are vertical or indeterminate.

This seems to be an impossible hyperbola. Are you sure the conjugate axis is 6 and not the semi conjugate axis?

Answer 2

Since a is 0, the asymptotes have infinite slope; that is, they are vertical lines. Without actually doing the calculations, I think they go through the foci, so the equations are: x=2 and x=8. This, of course, is a degenerate hyperbola.