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.?
Rewrite the equation in General Cartesian Form and then use the conditions of the discriminant to make the identification.
From the reference, the General Cartesian Form is:
The Discriminant is:
The conditions stated in the reference are:
A special case of this is, 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