# 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?

##### 1 Answer

The reference Hyperbola says that you are asking for the equation of a hyperbola.

#### Explanation:

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 [2] to equation [3]:

Substitute 4 for h into equation [3] and then solve for b:

Substitute these values into equation [1]:

Equation [2] is the answer; it represents a hyperbola.