# How do you identify the following equation x^2 + y^2 = 16 as that of a line, a circle, an ellipse, a parabola, or a hyperbola.?

Mar 25, 2016

The equation is that of a circle

#### Explanation:

First, move all terms on 1 side of the equation...
The equation will be in the form

$a {x}^{2} + b {y}^{2} + c x + \mathrm{dy} + e = 0$

If both $a$ and $b$ are 0, then we are dealing with a line.
If either $a$ or $b$ is 0 (but not both), then we are dealing with a parabola.
If $a$ and $b$ have different signs, then we are dealing with a hyperbola
If $a$ and $b$ are equal, then we are dealing with a circle
If $a$ and $b$ have the same signs but with different absolute value, then we are dealing with an ellipse