Question

identify the following equation x^2-y^2=4 as that of a line, a circle, an ellipse, a parabola, or a hyperbola

Answer 1

Hyperbola.

Explanation:

A line has no squared variables, so we know right away that is not the answer.

A parabola only has one variable squared, also not the case

a circle and ellipse have one variable squared divided by some number squared, ADDED to another set like that, so not this, since they are being subtracted.

This leaves hyperbola as the only possibility left.

Also, it is worth adding that each of these conic sections has a number on the other side of the equation, this has to be positive. If they are negative multiply the whole function by -1 (or divide it. you get the same result)