How do you find the equation of the following conic section and identify it given: All points such that the difference of the distance to the points (2,2) and (6,2) equals 2?
The reference Hyperbola says that you are asking for the equation of a hyperbola.
Because the foci are horizontally oriented, we shall use the standard form for a horizontal transverse axis:
We are given that the difference of the distance between the two points is 2. The reference tells us that this can be used to find the value of a:
The foci for this type are located at
Using the foci,
To find the value of h , add equation  to equation :
Substitute 4 for h into equation  and then solve for b:
Substitute these values into equation :
Equation  is the answer; it represents a hyperbola.