Question

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.?

Answer 1

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

`ax^2 + by^2 +cx + 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