# How do you identify the following equation #x^2 - y^2 = 4# as that of a line, a circle, an ellipse, a parabola, or a hyperbola.?

##### 1 Answer

Rewrite the equation in General Cartesian Form and then use the conditions of the discriminant to make the identification.

#### Explanation:

From the reference, the General Cartesian Form is:

The Discriminant is:

The conditions stated in the reference are:

If

A special case of this is, if

If

If

A special case of this is, if A + C = 0, then the equation represents a rectangular hyperbola.

Rewrite the given equation in General Cartesian Form:

Matching the coefficients in the general form:

Compute the discriminant:

The discriminant is greater than 0, therefore, the equation represents a hyperbola but, because