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.?

1 Answer
Mar 25, 2016

Answer:

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