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

##### 1 Answer

Jul 1, 2016

It is a hyperbola.

#### Explanation:

The general second degree equation can be written as

To identify the graph by inspection of equation complete any squares if necessary so that the variables are on one side and the constant is on the right hand side of the equation. Check against the following:

- Line

Squared term of neither variable is present. - Circle

Squared terms of both variables are present, both are positive and both have the same coefficient. The right hand side is positive. - Ellipse

Squared terms of both variables are present, both are positive and both have different coefficients. The right hand side is positive. - Parabola

Both variables are present but only one is squared. - Hyperbola

Squared terms of both variables are present, but one is positive and the other is negative. The coefficients may or may not be the same. The right hand side is not zero.

For 3, 4, and 5.

The general equation reduces to

which is a hyperbola if

A parabola has

For the given equation

graph{xy=4 [-10, 10, -5, 5]}